Refine
Has Fulltext
- yes (248)
Is part of the Bibliography
- yes (248)
Year of publication
Document Type
- Doctoral Thesis (140)
- Journal article (106)
- Master Thesis (1)
- Other (1)
Keywords
- Monte-Carlo-Simulation (12)
- Supersymmetrie (12)
- Topologischer Isolator (12)
- Blazar (10)
- topological insulators (10)
- Aktiver galaktischer Kern (8)
- Astrophysik (8)
- Elementarteilchenphysik (8)
- LHC (8)
- physics (8)
Institute
- Institut für Theoretische Physik und Astrophysik (248) (remove)
Sonstige beteiligte Institutionen
It is natural to consider the possibility that the most energetic particles detected (> 10^18 eV), ultra-high-energy cosmic rays (UHECRs), are originated at the most luminous transient events observed (> 10^52 erg s^-1), gamma-ray bursts (GRBs). As a result of the interaction of highly-accelerated, magnetically-confined protons and ions with the photon field inside the burst, both neutrons and UHE neutrinos are expected to be created: the former escape the source and beta-decay into protons which propagate to Earth, where they are detected as UHECRs, while the latter, if detected, would constitute the smoking gun of hadronic acceleration in the sources.
Recently, km-scale neutrino telescopes such as IceCube have finally reached the sensitivities required to probe the neutrino predictions of some of the existing GRB models. On that account, we present here a revised, self-consistent model of joint UHE proton and neutrino production at GRBs that includes a state-of-the-art, improved numerical calculation of the neutrino flux (NeuCosmA); that uses a generalised UHECR emission model where some of the protons in the sources are able to "leak out" of their magnetic confinement before having interacted; and that takes into account the energy losses of the protons during their propagation to Earth. We use our predictions to take a close look at the cosmic ray-neutrino connection and find that the current UHECR observations by giant air shower detectors, together with the upper bounds on the flux of neutrinos from GRBs, are already sufficient to put tension on several possibilities of particle emission and propagation, and to point us towards some requirements that should be fulfilled by GRBs if they are to be the sources of the UHECRs. We further refine our analysis by studying a dynamical burst model, where we find that the different particle species originate at distinct stages of the expanding GRB, each under particular conditions. Finally, we consider a possibility of new physics: the effect of neutrino decay in the flux of UHE neutrinos from GRBs. On the whole, our results demonstrate that self-consistent models of particle production are now integral to the advancement of the field, given that the full picture of the UHE Universe will only emerge as a result of looking at the multi-messenger sky, i.e., at gamma-rays, cosmic rays, and neutrinos simultaneously.
A novel magnetic ground state is reported for the Hubbard Hamiltonian in strained graphene. When the chemical potential lies close to the Dirac point, the ground state exhibits locally both the Neel and ferromagnetic orders, even for weak Hubbard interaction. Whereas the Neel order parameter remains of the same sign in the entire system, the magnetization at the boundary takes the opposite sign from the bulk. The total magnetization vanishes this way, and the magnetic ground state is globally only an antiferromagnet. This peculiar ordering stems from the nature of the strain-induced single-particle zero-energy states, which have support on one sublattice of the honeycomb lattice in the bulk, and on the other sublattice near the boundary of a finite system. We support our claim with the self-consistent numerical calculation of the order parameters, as well as by the Monte Carlo simulations of the Hubbard model in both uniformly and nonuniformly strained honeycomb lattice. The present result is contrasted with the magnetic ground state of the same Hubbard model in the presence of a true magnetic field (and for vanishing Zeeman coupling), which is exclusively Neel ordered, with zero local magnetization everywhere in the system.
In this thesis, we investigate aspects of the physics of heavy-fermion systems and correlated topological insulators.
We numerically solve the interacting Hamiltonians that model the physical systems using quantum Monte Carlo algorithms
to access both ground-state and finite-temperature observables.
Initially, we focus on the metamagnetic transition in the Kondo lattice model for heavy fermions.
On the basis of the dynamical mean-field theory and the dynamical cluster approximation,
our calculations point towards a continuous transition, where the signatures of metamagnetism are linked to a Lifshitz transition of heavy-fermion bands.
In the second part of the thesis, we study various aspects of magnetic pi fluxes in the Kane-Mele-Hubbard model of a correlated topological insulator.
We describe a numerical measurement of the topological index, based on the localized mid-gap states that are provided by pi flux insertions.
Furthermore, we take advantage of the intrinsic spin degree of freedom of a pi flux to devise instances of interacting quantum spin systems.
In the third part of the thesis, we introduce and characterize the Kane-Mele-Hubbard model on the pi flux honeycomb lattice.
We place particular emphasis on the correlations effects along the one-dimensional boundary of the lattice and
compare results from a bosonization study with finite-size quantum Monte Carlo simulations.
It has been argued that the emergence of roughly periodic orientation preference maps (OPMs) in the primary visual cortex (V1) of carnivores and primates can be explained by a so-called statistical connectivity model. This model assumes that input to V1 neurons is dominated by feed-forward projections originating from a small set of retinal ganglion cells (RGCs). The typical spacing between adjacent cortical orientation columns preferring the same orientation then arises via Moire 'Interference between hexagonal ON/OFF RGC mosaics. While this Moire-Interference critically depends on long-range hexagonal order within the RGC mosaics, a recent statistical analysis of RGC receptive field positions found no evidence for such long-range positional order. Hexagonal order may be only one of several ways to obtain spatially repetitive OPMs in the statistical connectivity model. Here, we investigate a more general requirement on the spatial structure of RGC mosaics that can seed the emergence of spatially repetitive cortical OPMs, namely that angular correlations between so-called RGC dipoles exhibit a spatial structure similar to that of OPM autocorrelation functions. Both in cat beta cell mosaics as well as primate parasol receptive field mosaics we find that RGC dipole angles are spatially uncorrelated. To help assess the level of these correlations, we introduce a novel point process that generates mosaics with realistic nearest neighbor statistics and a tunable degree of spatial correlations of dipole angles. Using this process, we show that given the size of available data sets, the presence of even weak angular correlations in the data is very unlikely. We conclude that the layout of ON/OFF ganglion cell mosaics lacks the spatial structure necessary to seed iso-orientation domains in the primary visual cortex.
Current theoretical studies of electronic correlations in transition metal oxides typically only account for the local repulsion between d-electrons even if oxygen ligand p-states are an explicit part of the effective Hamiltonian. Interatomic interactions such as U-pd between d- and (ligand) p-electrons, as well as the local interaction between p-electrons, are neglected. Often, the relative d-p orbital splitting has to be adjusted 'ad hoc' on the basis of the experimental evidence. By applying the merger of local density approximation and dynamical mean field theory to the prototypical case of the three-band Emery dp model for the cuprates, we demonstrate that, without any 'ad hoc' adjustment of the orbital splitting, the charge transfer insulating state is stabilized by the interatomic interaction U-pd. Our study hence shows how to improve realistic material calculations that explicitly include the p-orbitals.
We report magnetotransport studies on a gated strained HgTe device. This material is a three-dimensional topological insulator and exclusively shows surface-state transport. Remarkably, the Landau-level dispersion and the accuracy of the Hall quantization remain unchanged over a wide density range (3×1011 cm−2<n<2×1012 cm−2). These observations imply that even at large carrier densities, the transport is surface-state dominated, where bulk transport would have been expected to coexist already. Moreover, the density dependence of the Dirac-type quantum Hall effect allows us to identify the contributions from the individual surfaces. A k⋅p model can describe the experiments but only when assuming a steep band bending across the regions where the topological surface states are contained. This steep potential originates from the specific screening properties of Dirac systems and causes the gate voltage to influence the position of the Dirac points rather than that of the Fermi level.
In this thesis, the broad band emission, especially in the gamma-ray and radio band, of the active galaxy IC 310 located in the Perseus cluster of galaxies was investigated. The main experimental methods were Cherenkov astronomy using the MAGIC telescopes and high resolution very
long baseline interferometry (VLBI) at radio frequencies (MOJAVE, EVN). Additionally, data
of the object in different energy bands were studied and a multi-wavelength campaign has been
organized and conducted. During the campaign, an exceptional bright gamma-ray flare at TeV
energies was found with the MAGIC telescopes. The results were compared to theoretical acceleration and emission models for explaining the high energy radiation of active galactic nuclei. Many open questions regarding the particle acceleration to very high energies in the jets of active galactic nuclei, the particle content of the jets, or how the jets are launched, were addressed in this thesis by investigating the variability of IC 310 in the very high energy band.
It is argued that IC310 was originally mis-classified as a head-tail radio galaxy. Instead,
it shows a variability behavior in the radio, X-ray, and gamma-ray band similar to the one
found for blazars. These are active galactic nuclei that are characterized by flux variability in all observed energy bands and at all observed time scales. They are viewed at a small angle between the jet axis and the line-of-sight. Thus, strong relativistic beaming influences the variability properties of blazars. Observations of IC 310 with the European VLBI Network helped to find limits for the angle between the jet axis and the line-of-sight, namely 10 deg - 20 deg. This places IC 310 at the borderline between radio galaxies (larger angles) and blazars (smaller angles).
During the gamma-ray outburst detected at the beginning of the multi-wavelength campaign, flux variability as short as minutes was measured. The spectrum during the flare can be described by a simple power-law function over two orders of magnitude in energy up to ~10 TeV. Compared to previous observations, no significant variability of the spectral shape was found. Together with the constraint on the viewing angle, this challenges the currently accepted models for particle acceleration at shock waves in the jets. Alternative models, such as stars moving through the jets, mini-jets in the jet caused, e.g., by reconnection events, or gap acceleration in a pulsar-like magnetosphere around the black hole were investigated. It was found that only the latter can explain all observational findings, which at least suggests that it could even be worthwhile to reconsider published investigations of AGN with this new knowledge in mind.
The first multi-wavelength campaign was successfully been conducted in 2012/2013, including
ground-based as well as space-based telescopes in the radio, optical, ultraviolet, X-ray, and
gamma-ray energy range. No pronounced variability was found after the TeV flare in any energy band. The X-ray data showed a slightly harder spectrum when the emission was brighter. The long-term radio light curve indicated a flickering flux variability, but no strong hint for a
new jet component was found from VLBI images of the radio jet. In any case, further analysis of the existing multi-wavelength data as well as complimentary measurements could provide further exciting insights, e.g., about the broad band spectral energy distribution.
Overall, it can be stated that IC 310 is a key object for research of active galactic nuclei in
the high-energy band due to its proximity and its peculiar properties regarding flux variability
and spectral behavior. Such objects are ideally suited for studying particle acceleration, jet
formation, and other physical effects and models which are far from being fully understood.
The origin of fermion mass hierarchies and mixings is one of the unresolved and most difficult problems in high-energy physics. One possibility to address the flavour problems is by extending the standard model to include a family symmetry. In the recent years it has become very popular to use non-Abelian discrete flavour symmetries because of their power in the prediction of the large leptonic mixing angles relevant for neutrino oscillation experiments. Here we give an introduction to the flavour problem and to discrete groups that have been used to attempt a solution for it. We review the current status of models in light of the recent measurement of the reactor angle, and we consider different model-building directions taken. The use of the flavons or multi-Higgs scalars in model building is discussed as well as the direct versus indirect approaches. We also focus on the possibility of experimentally distinguishing flavour symmetry models by means of mixing sum rules and mass sum rules. In fact, we illustrate in this review the complete path from mathematics, via model building, to experiments, so that any reader interested in starting work in the field could use this text as a starting point in order to obtain a broad overview of the different subject areas.
The nature of dark matter and the origin of the baryon asymmetry are two of the deepest mysteries of modern particle physics. In the absence of hints regarding a possible solution to these mysteries, many approaches have been developed to tackle them simultaneously leading to very diverse and rich models. We give a short review where we describe the general features of some of these models and an overview on the general problem. We also propose a diagrammatic notation to label the different models.
Density functional theory (DFT) is applied to study the atomic, electronic, and spin structures of the Au monolayer at the Ge(111) surface. It is found that the theoretically determined most stable atomic geometry is described by the conjugated honeycomb-chained-trimer (CHCT) model, in a very good agreement with experimental data. The calculated electronic structure of the system, being in qualitatively good agreement with the photoemission measurements, shows fingerprints of the many-body effects (self-interaction corrections) beyond the LDA or GGA approximations. The most interesting property of this surface system is the large spin splitting of its metallic surface bands and the undulating spin texture along the hexagonal Fermi contours, which highly resembles the spin texture at the Dirac state of the topological insulator Bi\(_{2}\)Te\(_{3}\). These properties make this system particularly interesting from both fundamental and technological points of view.
Recent theoretical studies employing density-functional theory have predicted BaBiO\(_{3}\) (when doped with electrons) and YBiO\(_{3}\) to become a topological insulator (TI) with a large topological gap (~0.7 eV). This, together with the natural stability against surface oxidation, makes the Bismuth-Oxide family of special interest for possible applications in quantum information and spintronics. The central question, we study here, is whether the hole-doped Bismuth Oxides, i.e. Ba\(_{1-X}\)K\(_{X}\)BiO\(_{3}\) and BaPb\(_{1-X}\)Bi\(_{X}\)O\(_{3}\), which are "high-Tc" bulk superconducting near 30 K, additionally display in the further vicinity of their Fermi energy E\(_{F}\) a topological gap with a Dirac-type of topological surface state. Our electronic structure calculations predict the K-doped family to emerge as a TI, with a topological gap above E\(_{F}\). Thus, these compounds can become superconductors with hole-doping and potential TIs with additional electron doping. Furthermore, we predict the Bismuth-Oxide family to contain an additional Dirac cone below E\(_{F}\) for further hole doping, which manifests these systems to be candidates for both electron-and hole-doped topological insulators.
We study a two-level system controlled in a discrete feedback loop, modeling both the system and the controller in terms of stochastic Markov processes. We find that the extracted work, which is known to be bounded from above by the mutual information acquired during measurement, has to be compensated by an additional energy supply during the measurement process itself, which is bounded by the same mutual information from below. Our results confirm that the total cost of operating an information engine is in full agreement with the conventional second law of thermodynamics. We also consider the efficiency of the information engine as a function of the cycle time and discuss the operating condition for maximal power generation. Moreover, we find that the entropy production of our information engine is maximal for maximal efficiency, in sharp contrast to conventional reversible heat engines.
Many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain "pseudopotential" Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z\(_3\) states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU(n) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.
Pulsars (in short for Pulsating Stars) are magnetized, fast rotating neutron stars. The basic picture of a pulsar describes it as a neutron star which has a rotation axis that is not aligned with its magnetic field axis. The emission is assumed to be generated near the magnetic poles of the neutron star and emitted along the open magnetic field lines. Consequently, the corresponding beam of photons is emitted along the magnetic field line axis. The non-alignment of both, the rotation and the magnetic field axis, results in the effect that the emission of the pulsar is only seen if its beam points towards the observer.
The emission from a pulsar is therefore perceived as being pulsed although its generation is not. This rather simple geometrical model is commonly referred to as Lighthouse Model and has been widely accepted. However, it does not deliver an explanation of the precise mechanisms behind the emission from pulsars (see below for more details).
Nowadays more than 2000 pulsars are known. They are observed at various wavelengths. Multiwavelength studies have shown that some pulsars are visible only at certain wavelengths while the emission from others can be observed throughout large parts of the electromagnetic spectrum. An example of the latter case is the Crab pulsar which is also the main object of interest in this thesis. Originating from a supernova explosion observed in 1054 A.D. and discovered in 1968, the Crab pulsar has been the central subject of numerous studies. Its pulsed emission is visible throughout the whole electromagnetic spectrum which makes it a key figure in understanding the possible mechanisms of multiwavelength emission from pulsars.
The Crab pulsar is also well known for its radio emission strongly varying on long as well as on short time scales. While long time scale behaviour from a pulsar is usually examined through the use of its average profile (a profile resulting from averaging of a large number of individual pulses resulting from single rotations), short time scale behaviour is examined via its single pulses. The short time scale anomalous behaviour of its radio emission is commonly referred to as Giant Pulses and represents the central topic of this thesis.
While current theoretical approaches place the origin of the radio emission from a pulsar like the Crab near its magnetic poles (Polar Cap Model) as already indicated by the Lighthouse model, its emission at higher frequencies, especially its gamma-ray emission, is assumed to originate further away in the geometrical region surrounding a pulsar which is commonly referred to as a pulsar magnetosphere (Outer Gap Model). Consequently, the respective emission regions are usually assumed not to be connected. However, past observational results from the Crab pulsar represent a contradiction to this assumption.
Radio giant pulses from the Crab pulsar have been observed to emit large amounts of energy on very short time scales implying small emission regions on the surface of the pulsar. Such energetic events might also leave a trace in the gamma-ray emission of the Crab pulsar.
The aim of this thesis is to search for this connection in the form of a correlation study between radio giant pulses and gamma-photons from the Crab pulsar.
To make such a study possible, a multiwavelength observational campaign was organized for which radio observations were independently applied for, coordinated and carried out with the Effelsberg radio telescope and the Westerbork Synthesis Radio Telescope and gamma-ray observations with the Major Atmospheric Imaging Cherenkov telescopes. The corresponding radio and gamma-ray data sets were reduced and the correlation analysis thereafter consisted of three different approaches:
1) The search for a clustering in the differences of the times of arrival of radio giant pulses and gamma-photons;
2) The search for a linear correlation between radio giant pulses and gamma-photons using the Pearson correlation approach;
3) A search for an increase of the gamma-ray flux around occurring radio giant pulses.
In the last part of the correlation study an increase of the number of gamma-photons centered on a radio giant pulse by about 17% (in contrast with the number of gamma-photons when no radio giant pulse occurs in the same time window) was discovered. This finding suggests that a new theoretical approach for the emission of young pulsars like the Crab pulsar, is necessary.
It is generally agreed upon the fact that the Standard Model of particle physics can only be viewed as an effective theory that needs to be extended as it leaves some essential questions unanswered. The exact realization of the necessary extension is subject to discussion. Supersymmetry is among the most promising approaches to physics beyond the Standard Model as it can simultaneously solve the hierarchy problem and provide an explanation for the dark matter abundance in the universe. Despite further virtues like gauge coupling unification and radiative electroweak symmetry breaking, minimal supersymmetric models cannot be the ultimate answer to the open questions of the Standard Model as they still do not incorporate neutrino masses and are besides heavily constrained by LHC data. This does, however, not derogate the beauty of the concept of supersymmetry. It is therefore time to explore non-minimal supersymmetric models which are able to close these gaps, review their consistency, test them against experimental data and provide prospects for future experiments.
The goal of this thesis is to contribute to this process by exploring an extraordinarily well motivated class of models which bases upon a left-right symmetric gauge group. While relaxing the tension with LHC data, those models automatically include the ingredients for neutrino masses.
We start with a left-right supersymmetric model at the TeV scale in which scalar \(SU(2)_R\) triplets are responsible for the breaking of left-right symmetry as well as for the generation of neutrino masses. Although a tachyonic doubly-charged scalar is present at tree-level in this kind of models, we show by performing the first complete one-loop evaluation that it gains a real mass at the loop level. The constraints on the predicted additional charged gauge bosons are then evaluated using LHC data, and we find that we can explain small excesses in the data of which the current LHC run will reveal if they are actual new physics signals or just background fluctuations. In a careful evaluation of the loop-corrected scalar potential we then identify parameter regions in which the vacuum with the phenomenologically correct symmetry-breaking properties is stable. Conveniently, those regions favour low left-right symmetry breaking scales which are accessible at the LHC.
In a slightly modified version of this model where a \(U(1)_R × U(1)_{B−L}\) gauge symmetry survives down to the TeV scale, we implement a minimal gauge-mediated supersymmetry breaking mechanism for which we calculate the boundary conditions in the presence of gauge kinetic mixing. We show how the presence of the extended gauge group raises the tree-level Higgs mass considerably so that the need for heavy supersymmetric spectra is relaxed. Taking the constraints from the Higgs sector into account, we then explore the LHC phenomenology of this model and point out where the expected collider signatures can be distinguished from standard scenarios.
In particular if neutrino masses are explained by low-scale seesaw mechanisms as is done throughout this work, there are potentially spectacular signals at low-energy experiments which search for charged lepton flavour violation. The last part of this thesis is dedicated to the detailed exploration of processes like μ → e γ, μ → 3 e or μ−e conversion in nuclei in a supersymmetric framework with an inverse seesaw mechanism. In particular, we disprove claims about a non-decoupling effect in Z-mediated three-body decays and study the prospects for discovering and distinguishing signals at near-future experiments. In this context we identify the possibility to deduce from ratios like BR(\(τ → 3 μ\))/BR(\(τ → μ e^+ e^−\)) whether the contributions from ν − W loops dominate over supersymmetric contributions or vice versa.
Das Magnetfeld der Sonne ist kein einfaches statisches Dipolfeld, sondern weist
wesentlich kompliziertere Strukturen auf. Wenn Rekonnexion die Topologie eines
Feldlinienbündels verändert, wird viel Energie frei, die zuvor im Magnetfeld
gespeichert war. Das abgetrennte Bündel wird mit dem damit verbundenen Plasma
mit großer Geschwindigkeit durch die Korona
von der Sonne weg bewegen. Dieser Vorgang wird als koronaler Massenauswurf
bezeichnet. Da diese Bewegung mit Geschwindigkeiten deutlich über der
Alfv\'en-Geschwindigkeit, der kritischen Geschwindigkeit im Sonnenwind,
erfolgen kann, bildet sich eine Schockfront, die durch den Sonnenwind
propagiert.
Satelliten, die die Bedingungen im Sonnenwind beobachten, detektieren beim
Auftreten solcher Schockfronten einen erhöhten Fluss von hochenergetischen
Teilchen. Mit Radioinstrumenten empfängt man zeitgleich elektromagnetische
Phänomene, die als Radiobursts bezeichnet werden, und ebenfalls für die
Anwesenheit energiereicher Teilchen sprechen. Daher, und aufgrund von
theoretischen Überlegungen liegt es nahe, anzunehmen, daß Teilchen an der
Schockfront beschleunigt werden können.
Die Untersuchung der Teilchenbeschleunigung an kollisionsfreien Schockfronten
ist aber noch aus einem zweiten Grund interessant. Die Erde wird kontinuierlich
von hochenergetischen Teilchen, die aus historischen Gründen als kosmische
Strahlung bezeichnet werden, erreicht. Die gängige Theorie für deren Herkunft
besagt, daß zumindest der galaktische Anteil durch die Beschleunigung an
Schockfronten, die durch Supernovae ausgelöst wurden, bis zu den beobachteten
hohen Energien gelangt sind. Das Problem bei der Untersuchung der Herkunft der
kosmischen Strahlung ist jedoch, daß die Schockfronten um Supernovaüberreste
aufgrund der großen Entfernung nicht direkt beobachtbar sind.
Es liegt dementsprechend nahe, die Schockbeschleunigung an den wesentlich
näheren und besser zu beobachtenden Schocks im Sonnensystem zu studieren, um so
Modelle und Simulationen entwickeln und testen zu können.
Die vorliegende Arbeit beschäftigt sich daher mit Simulationen von
Schockfronten mit Parametern, die etwa denen von CME getriebenen Schocks
entsprechen. Um die Entwicklung der Energieverteilung der Teilchen zu studieren,
ist ein kinetischer Ansatz nötig. Dementsprechend wurden die Simulationen mit
einem Particle-in-Cell Code durchgeführt. Die Herausforderung ist dabei die
große Spanne zwischen den mikrophysikalischen Zeit- und Längenskalen, die aus
Gründen der Genauigkeit und numerischen Stabilität aufgelöst werden müssen und
den wesentlich größeren Skalen, die die Schockfront umfasst und auf der
Teilchenbeschleunigung stattfindet.
Um die Stabilität und physikalische Aussagekraft der Simulationen
sicherzustellen, werden die numerischen Bausteine mittels Testfällen, deren
Verhalten bekannt ist, gründlich auf ihre Tauglichkeit und korrekte
Implementierung geprüft.
Bei den resultierenden Simulationen wird das Zutreffen von analytischen
Vorhersagen (etwa die Einhaltung der Sprungbedingungen) überprüft. Auch die
Vorhersagen einfacherer Plasmamodelle, etwa für das elektrostatischen
Potential an der Schockfront, das man auch aus einer Zwei-Fluid-Beschreibung
erhalten kann, folgen automatisch aus der selbstkonsistenten, kinetischen
Beschreibung. Zusätzlich erhält man Aussagen über das Spektrum und die Bahnen
der beschleunigten Teilchen.
Bis heute ist nicht bekannt, in welcher Umgebung die schwersten Elemente durch Neutroneneinfangprozesse entstehen. Es gibt zwei mögliche Szenarien, die in der Literatur diskutiert werden: Supernova-Explosionen und Neutronensternverschmelzungen. Beide tragen zur Elementproduktion bei. Welches Szenario aber die dominierende Umgebung ist, bleibt umstritten. Mehrere Fakten sprechen für Supernova-Explosionen als Entstehungsorte: Wenn ein massereicher Stern kollabiert und anschließend explodiert, sind die Temperatur und die Dichte so hoch, dass Neutronen von den bereits bestehenden Elementen eingefangen und angelagert werden können. Obwohl in Simulationen mit kugelsymmetrischen Modellen nur protonen- reiche Auswürfe entstehen, kann es in asymmetrischen Explosionen aufgrund der Rotation und der Magnetfelder vermutlich zu einem neutronenreichen Auswurf kommen. Dieser ist hoch genug, dass der schnelle Neutroneneinfang auftreten kann. In dieser Arbeit habe ich daher die Überreste solcher Explosionen untersucht, um nach Asymmetrien und ihren möglichen Auswirkungen auf die Element-Entstehung und Verteilung zu suchen. Dafür wurden die beiden Supernova-Überreste CTB 109 und RCW 103 ausgewählt. CTB 109 besitzt im Zentrum einen anomale Röntgenpulsar, also einen Neutronenstern mit hohem Magnetfeld und starker Rotation, die durch Asymmetrien hervorgerufen worden sein könnten. Auch RCW 103 hat vermutlich einen solchen Pulsar als zentrale Quelle. Beide Überreste sind noch recht jung und befinden sich in ihrer Sedov-Taylor Phase. Die Distanz zur Erde beträgt für beide Überreste ungefähr 3 kpc, womit sie in der näheren Umgebung der Erde zu finden sind. Die Elemente bis zur Eisengruppe haben ihre bekanntesten Linien im Bereich der Röntgenstrahlung. Deswegen wurden für diese Arbeit archivierte Daten des Satelliten XMM-Newton ausgewählt und die Spektren in definierten Regionen in den bei- den Supernova-Überresten mit den EPIC MOS-Kameras ausgewertet. Die heutigen Röntgensatelliten haben jedoch keine ausreichende Sensitivität, um die schwersten Elemente zu detektieren. In den Spektren der beiden Überreste wurden deshalb vorwiegend die Elemente Silizium und Magnesium gefunden, in CTB 109 auch Neon. Elemente mit höheren Massezahlen konnten leider nicht signifikant aus dem Hintergrund herausgefiltert werden. Deutlich sind die Peaks der drei Elementen sichtbar, aber auch Schwefel ist in den Regionen mit hohen Zählraten zu entdecken. Für bei- de Supernova-Überreste wurde der beste Fit mit dem Modell vpshock gefunden. In diesem Modell wird ein Plasma angenommen, das bei konstanter Temperatur plan-parallel geschockt wird. Um diesen Fit zu erzielen wurden die Parameter für die Elemente Fe, S, Si, Mg, O und Ne variiert. Die restlichen Elemente wurden auf die solare Häufigkeit festgelegt. Bei CTB 109 befinden sich die Temperaturen (kT) in den Regionen mit hohen Zählraten im Bereich zwischen 0.6 und 0.7 keV und liegen damit im selben Bereich, der bereits mit anderen Teleskopen für CTB 109 gefunden wurde. In den Regionen mit niedrigen Zählraten liegen die Temperaturen etwas tiefer mit 0.3-0.4 keV. Im Supernova-Überrest RCW 103 wurde nur eine Region mit hoher Zählrate analysiert und eine Temperatur von 0.57 keV gefunden, während in der Region mit niedriger Zählrate die Temperatur kT = 0.36 ± 0.08 keV beträgt. Beide Werte passen zu den Werten in CTB 109. Die einzelnen Elementlinien wurden zusätzlich mit einer Gauß-Verteilung angepasst und die Flüsse ermittelt. Diese wurden in Intensitätskarten aufgetragen, in denen die unterschiedlichen Verteilungen der Elemente über den Supernova-Überrest zu sehen sind. Während Silizium in einigen wenigen Regionen geklumpt auftritt, ist Magnesium über die Überreste verteilt und hat in einigen Regionen höhere Werte als Silizium. Das lässt den Schluss zu, dass die beiden Elemente auf unterschiedliche Weise aus der Explosion herausgeschleudert wurden. Die Verteilung ist hier durchaus asymmetrisch, es ist jedoch nicht möglich dies auf eine asymmetrische Explosion der Supernova zurückzuführen. Dafür müssen mehr als zwei Supernova-Überreste mit dieser Methode untersucht werden und mit einer noch nicht vorhandenen Theorie zur Verteilung der Elemente in Überresten verglichen werden. Im direkten Vergleich der beiden bisher untersuchten Supernova-Überreste CTB 109 und RCW 103 sieht man, dass die beiden Überreste sich sehr in der Temperatur und der Verteilung der Elemente ähneln. Das lässt auf eine einheitliche Ausbreitung der Elemente innerhalb der Supernova-Überreste schließen. Silizium wird aufgrund der Explosion in fingerartigen Strukturen, die Rayleigh-Taylor-Instabilitäten, nach außen transportiert. Dabei bildet es Klumpen, die mit den weiter außen liegenden Schalen reagieren. Magnesium und Neon hingegen werden hauptsächlich in den Brennphasen vor der Explosion und in den äußeren Schichten des Sterns, der Zwiebelschalenstruktur, produziert. Dadurch ist eine ausgedehnte Verteilung zu er- warten. Diese Verteilungen der drei Elemente ist in dieser Arbeit bestätigt worden. Während Magnesium und Neon über den gesamten Überrest hohe Flüsse aufweisen, ist Silizium sehr lokal im Lobe von CTB 109 und im hellen Süden von RCW 103 zu finden. Mit zukünftigen Röntgenteleskopen, die eine höhere räumliche Auflösung ermöglichen, könnten die beobachteten Zusammenhänge zwischen der asymmetrischen Elementverteilung im Supernovaüberrest und den Mechanismen der Elemententstehung in der Supernova weiter untersucht werden.
In the field of spintronics, spin manipulation and spin transport are the main principles that need to be implemented. The main focus of this thesis is to analyse semiconductor systems where high fidelity in these principles can be achieved. To this end, we use numerical methods for precise results, supplemented by simpler analytical models for interpretation.
The material system of 2D topological insulators, HgTe/CdTe quantum wells, is interesting not only because it provides a topologically distinct phase of matter, physically manifested in its protected transport properties, but also since within this system, ballistic transport of high quality can be realized, with Rashba spin-orbit coupling and electron densities that are tunable by electrical gating. Extending the Bernvevig-Hughes-Zhang model for 2D topological insulators, we derive an effective four-band model including Rashba spin-orbit terms due to an applied potential that breaks the spatial inversion symmetry of the quantum well. Spin transport in this system shows interesting physics because the effects of Rashba spin-orbit terms and the intrinsic Dirac-like spin-orbit terms compete. We show that the resulting spin Hall signal can be dominated by the effect of Rashba spin-orbit coupling. Based on spin splitting due to the latter, we propose a beam splitter setup for all-electrical generation and detection of spin currents. Its working principle is similar to optical birefringence. In this setup, we analyse spin current and spin polarization signals of different spin vector components and show that large in-plane spin polarization of the current can be obtained. Since spin is not a conserved quantity of the model,
we first analyse the transport of helicity, a conserved quantity even in presence of Rashba spin-orbit terms. The polarization defined in terms of helicity is related to in-plane polarization of the physical spin.
Further, we analyse thermoelectric transport in a setup showing the spin Hall effect. Due to spin-orbit coupling, an applied temperature gradient generates a transverse spin current, i.e. a spin Nernst effect, which is related to the spin Hall effect by a Mott-like relation. In the metallic energy regimes, the signals are qualitatively explained by simple analytic models. In the insulating regime, we observe a spin Nernst signal that originates from the finite-size induced overlap of edge states.
In the part on methods, we discuss two complementary methods for construction of effective semiconductor models, the envelope function theory and the method of invariants. Further, we present elements of transport theory, with some emphasis on spin-dependent signals. We show the connections of the adiabatic theorem of quantum mechanics to the semiclassical theory of electronic transport and to the characterization of topological phases. Further, as application of the adiabatic theorem to a control problem, we show that universal control of a single spin in a heavy-hole quantum dot is experimentally realizable without breaking time reversal invariance,
but using a quadrupole field which is adiabatically changed as control knob. For experimental realization, we propose a GaAs/GaAlAs quantum well system.
Over the last decade, the field of topological insulators has become one of the most vivid areas in solid state physics. This novel class of materials is characterized by an insulating bulk gap, which, in two-dimensional, time-reversal symmetric systems, is closed by helical edge states. The latter make topological insulators promising candidates for applications in high fidelity spintronics and topological quantum computing. This thesis contributes to bringing these fascinating concepts to life by analyzing transport through heterostructures formed by two-dimensional topological insulators in contact with metals or superconductors. To this end, analytical and numerical calculations are employed. Especially, a generalized wave matching approach is used to describe the edge and bulk states in finite size tunneling junctions on the same footing.
The numerical study of non-superconducting systems focuses on two-terminal metal/topological
insulator/metal junctions. Unexpectedly, the conductance signals originating from the bulk and
the edge contributions are not additive. While for a long junction, the transport is determined
purely by edge states, for a short junction, the conductance signal is built from both bulk and
edge states in a ratio, which depends on the width of the sample. Further, short junctions show
a non-monotonic conductance as a function of the sample length, which distinguishes the topologically non-trivial regime from the trivial one. Surprisingly, the non-monotonic conductance of the topological insulator can be traced to the formation of an effectively propagating solution, which is robust against scalar disorder.
The analysis of the competition of edge and bulk contributions in nanostructures is extended to transport through topological insulator/superconductor/topological insulator tunneling junctions. If the dimensions of the superconductor are small enough, its evanescent bulk modes
can couple edge states at opposite sample borders, generating significant and tunable crossed
Andreev reflection. In experiments, the latter process is normally disguised by simultaneous
electron transmission. However, the helical edge states enforce a spatial separation of both competing processes for each Kramers’ partner, allowing to propose an all-electrical measurement
of crossed Andreev reflection.
Further, an analytical study of the hybrid system of helical edge states and conventional superconductors in finite magnetic fields leads to the novel superconducting quantum spin Hall effect. It is characterized by edge states. Both the helicity and the protection against scalar disorder of these edge states are unaffected by an in-plane magnetic field. At the same time its superconducting gap and its magnetotransport signals can be tuned in weak magnetic fields, because the combination of helical edge states and superconductivity results in a giant g-factor. This is manifested in a non-monotonic excess current and peak splitting of the dI/dV characteristics as a function of the magnetic field. In consequence, the superconducting quantum spin Hall effect is an effective generator and detector for spin currents.
The research presented here deepens the understanding of the competition of bulk and edge
transport in heterostructures based on topological insulators. Moreover it proposes feasible experiments to all-electrically measure crossed Andreev reflection and to test the spin polarization of helical edge states.
The architecture of iso-orientation domains in the primary visual cortex (V1) of placental carnivores and primates apparently follows species invariant quantitative laws. Dynamical optimization models assuming that neurons coordinate their stimulus preferences throughout cortical circuits linking millions of cells specifically predict these invariants. This might indicate that V1's intrinsic connectome and its functional architecture adhere to a single optimization principle with high precision and robustness. To validate this hypothesis, it is critical to closely examine the quantitative predictions of alternative candidate theories. Random feedforward wiring within the retino-cortical pathway represents a conceptually appealing alternative to dynamical circuit optimization because random dimension-expanding projections are believed to generically exhibit computationally favorable properties for stimulus representations. Here, we ask whether the quantitative invariants of V1 architecture can be explained as a generic emergent property of random wiring. We generalize and examine the stochastic wiring model proposed by Ringach and coworkers, in which iso-orientation domains in the visual cortex arise through random feedforward connections between semi-regular mosaics of retinal ganglion cells (RGCs) and visual cortical neurons. We derive closed-form expressions for cortical receptive fields and domain layouts predicted by the model for perfectly hexagonal RGC mosaics. Including spatial disorder in the RGC positions considerably changes the domain layout properties as a function of disorder parameters such as position scatter and its correlations across the retina. However, independent of parameter choice, we find that the model predictions substantially deviate from the layout laws of iso-orientation domains observed experimentally. Considering random wiring with the currently most realistic model of RGC mosaic layouts, a pairwise interacting point process, the predicted layouts remain distinct from experimental observations and resemble Gaussian random fields. We conclude that V1 layout invariants are specific quantitative signatures of visual cortical optimization, which cannot be explained by generic random feedforward-wiring models.
We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling K\(_2\), which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iridate Na\(_2\)IrO\(_3\), and may also play a role in \(\alpha\)-RuCl\(_3\) and Li\(_2\)IrO\(_3\). This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in Na\(_2\)IrO\(_3\). Moreover, the minimal K\(_1\) - K\(_2\) model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.
Topological insulators are electronic phases that insulate in the bulk and accommodate a peculiar, metallic edge liquid with a spin-dependent dispersion.
They are regarded to be of considerable future use in spintronics and for quantum computation.
Besides determining the intrinsic properties of this rather novel electronic phase, considering its combination with well-known physical systems can generate genuinely new physics.
In this thesis, we report on such combinations including topological insulators. Specifically, we analyze an attached Rashba impurity, a Kondo dot in the two channel setup, magnetic impurities on the surface of a strong three-dimensional topological insulator, the proximity coupling of the latter system to a superconductor, and hybrid systems consisting of a topological insulator and a semimetal.
Let us summarize our primary results.
Firstly, we determine an analytical formula for the Kondo cloud and describe its possible detection in current correlations far away from the Kondo region.
We thereby rely on and extend the method of refermionizable points.
Furthermore, we find a class of gapless topological superconductors and semimetals, which accommodate edge states that behave similarly to the ones of globally gapped topological phases. Unexpectedly, we also find edge states that change their chirality when affected by sufficiently strong disorder.
We regard the presented research helpful in future classifications and applications of systems containing topological insulators, of which we propose some examples.
In the course of the growth of the Internet and due to increasing availability of data, over the last two decades, the field of network science has established itself as an own area of research. With quantitative scientists from computer science, mathematics, and physics working on datasets from biology, economics, sociology, political sciences, and many others, network science serves as a paradigm for interdisciplinary research.
One of the major goals in network science is to unravel the relationship between topological graph structure and a network’s function. As evidence suggests, systems from the same fields, i.e. with similar function, tend to exhibit similar structure. However, it is still vague whether a similar graph structure automatically implies likewise function. This dissertation aims at helping to bridge this gap, while particularly focusing on the role of triadic structures.
After a general introduction to the main concepts of network science, existing work devoted to the relevance of triadic substructures is reviewed. A major challenge in modeling triadic structure is the fact that not all three-node subgraphs can be specified independently
of each other, as pairs of nodes may participate in multiple of those triadic subgraphs.
In order to overcome this obstacle, we suggest a novel class of generative network models based on so called Steiner triple systems. The latter are partitions of a graph’s vertices into pair-disjoint triples (Steiner triples). Thus, the configurations on Steiner triples can be specified independently of each other without overdetermining the network’s link
structure.
Subsequently, we investigate the most basic realization of this new class of models. We call it the triadic random graph model (TRGM). The TRGM is parametrized by a probability distribution over all possible triadic subgraph patterns. In order to generate a network instantiation of the model, for all Steiner triples in the system, a pattern is drawn from the distribution and adjusted randomly on the Steiner triple. We calculate the degree distribution of the TRGM analytically and find it to be similar to a Poissonian distribution. Furthermore, it is shown that TRGMs possess non-trivial triadic structure. We discover inevitable correlations in the abundance of certain triadic subgraph
patterns which should be taken into account when attributing functional relevance to particular motifs – patterns which occur significantly more frequently than expected at random. Beyond, the strong impact of the probability distributions on the Steiner triples on the occurrence of triadic subgraphs over the whole network is demonstrated. This interdependence allows us to design ensembles of networks with predefined triadic substructure. Hence, TRGMs help to overcome the lack of generative models needed for assessing the relevance of triadic structure.
We further investigate whether motifs occur homogeneously or heterogeneously distributed over a graph. Therefore, we study triadic subgraph structures in each node’s neighborhood individually. In order to quantitatively measure structure from an individual node’s perspective, we introduce an algorithm for node-specific pattern mining for both directed unsigned, and undirected signed networks. Analyzing real-world datasets, we find that there are networks in which motifs are distributed highly heterogeneously, bound to the proximity of only very few nodes. Moreover, we observe indication for the potential sensitivity of biological systems to a targeted removal of these critical vertices. In addition, we study whole graphs with respect to the homogeneity and homophily of their node-specific triadic structure. The former describes the similarity of subgraph distributions in the neighborhoods of individual vertices. The latter quantifies whether connected vertices
are structurally more similar than non-connected ones. We discover these features to be characteristic for the networks’ origins. Moreover, clustering the vertices of graphs regarding their triadic structure, we investigate structural groups in the neural network of C. elegans, the international airport-connection network, and the global network of diplomatic sentiments between countries. For the latter we find evidence for the instability of triangles considered socially unbalanced according to sociological theories.
Finally, we utilize our TRGM to explore ensembles of networks with similar triadic substructure in terms of the evolution of dynamical processes acting on their nodes. Focusing on oscillators, coupled along the graphs’ edges, we observe that certain triad motifs impose a clear signature on the systems’ dynamics, even when embedded in a larger
network structure.
One of the most popular extensions of the SM is Supersymmetry (SUSY). It is a symmetry relating fermions and bosons and also the only feasible extension to the symmetries of spacetime. With SUSY it is then possible to explain some of the open questions left by the SM while at the same time opening the possibility of gauge unification at a high scale. SUSY theories require the addition of new particles, in particular an extra Higgs doublet and at least as many new scalars as fermions in the SM. Much in the same way that the Higgs boson breaks SU (2)L symmetry, these new scalars can break any symmetry for which they carry a charge through spontaneous symmetry breaking.
Let us assume there is a local minimum of the potential that reproduces the correct phenomenol- ogy for a parameter point of a given model. By exploring whether there are other deeper minima with VEVs that break symmetries we want to conserve, like SU (3)C or U (1)EM , it is possible to exclude regions of parameter space where that happens. The local minimum with the correct phenomenology might still be metastable, so it is also necessary to calculate the probability of tunneling between minima.
In this work we propose and apply a framework to constrain the parameter space of models with many scalars through the minimization of the one-loop eff e potential and the calculation of tunneling times at zero and non zero temperature.After a brief discussion about the shortcomings of the SM and an introduction of the basics of SUSY, we introduce the theory and numerical methods needed for a successful vacuum stability analysis. We then present Vevacious, a public code where we have implemented our proposed framework. Afterwards we go on to analyze three interesting examples.
For the constrained MSSM (CMSSM) we explore the existence of charge- and color- breaking (CCB) minima and see how it constraints the phenomenological relevant region of its parameter space at T = 0. We show that the regions reproducing the correct Higgs mass and the correct relic density for dark matter all overlap with regions suffering from deeper CCB minima.
Inspired by the results for the CMSSM, we then consider the natural MSSM and check the region of parameter space consistent with the correct Higgs mass against CCB minima at T /= 0. We find that regions of parameter space with CCB minima overlap significantly with that reproducing the correct Higgs mass. When thermal eff are considered the majority of such points are then found to have a desired symmetry breaking minimum with very low survival probability. In both these studies we find that analytical conditions presented in the literature fail in dis- criminating regions of parameter space with CCB minima. We also present a way of adapting our framework so that it runs quickly enough for use with parameter fit studies.
Lastly we show a different example of using vacuum stability in a phenomenological study. For the BLSSM we investigate the violation of R-parity through sneutrino VEVs and where in parameter space does this happen. We find that previous analyses in literature fail to identify regions with R-parity conservation by comparing their results to our full numerical analysis.
This thesis deals with quantum Monte Carlo simulations of correlated low dimensional electron systems. The correlation that we have in mind is always given by the Hubbard type electron electron interaction in various settings. To facilitate this task, we develop the necessary methods in the first part. We develop the continuous time interaction expansion quantum algorithm in a manner suitable for the treatment of effective and non-equilibrium problems. In the second part of this thesis we consider various applications of the algorithms. First we examine a correlated one-dimensional chain of electrons that is subject to some form of quench dynamics where we suddenly switch off the Hubbard interaction. We find the light-cone-like Lieb-Robinson bounds and forms of restricted equilibration subject to the conserved quantities. Then we consider a Hubbard chain subject to Rashba spin-orbit coupling in thermal equilibrium. This system could very well be realized on a surface with the help of metallic adatoms. We find that we can analytically connect the given model to a model without spin-orbit coupling. This link enabled us to interpret various results for the standard Hubbard model, such as the single-particle spectra, now in the context of the Hubbard model with Rashba spin-orbit interaction. And finally we have considered a magnetic impurity in a host consisting of a topological insulator. We find that the impurity still exhibits the same features as known from the single impurity Anderson model. Additionally we study the effects of the impurity in the bath and we find that in the parameter regime where the Kondo singlet is formed the edge state of the topological insulator is rerouted around the impurity.
Accessing topological superconductivity via a combined STM and renormalization group analysis
(2015)
The search for topological superconductors has recently become a key issue in condensed matter physics, because of their possible relevance to provide a platform for Majorana bound states, non-Abelian statistics, and quantum computing. Here we propose a new scheme which links as directly as possible the experimental search to a material-based microscopic theory for topological superconductivity. For this, the analysis of scanning tunnelling microscopy, which typically uses a phenomenological ansatz for the superconductor gap functions, is elevated to a theory, where a multi-orbital functional renormalization group analysis allows for an unbiased microscopic determination of the material-dependent pairing potentials. The combined approach is highlighted for paradigmatic hexagonal systems, such as doped graphene and water-intercalated sodium cobaltates, where lattice symmetry and electronic correlations yield a propensity for a chiral singlet topological superconductor. We demonstrate that our microscopic material-oriented procedure is necessary to uniquely resolve a topological superconductor state.
This Letter presents measurements of correlated production of nearby jets in Pb+Pb collisions at \(\sqrt S_{NN}\)=2.76 TeV using the ATLAS detector at the Large Hadron Collider. The measurement was performed using 0.14 nb\(^{-1}\) of data recorded in 2011. The production of correlated jet pairs was quantified using the rate, R\(_{ΔR}\), of “neighbouring” jets that accompany “test” jets within a given range of angular distance, ΔR , in the pseudorapidity–azimuthal angle plane. The jets were measured in the ATLAS calorimeter and were reconstructed using the anti-k\(_t\) algorithm with radius parameters d=0.2, 0.3, and 0.4. R\(_{ΔR}\) was measured in different Pb+Pb collision centrality bins, characterized by the total transverse energy measured in the forward calorimeters. A centrality dependence of R\(_{ΔR}\) is observed for all three jet radii with R\(_{ΔR}\) found to be lower in central collisions than in peripheral collisions. The ratios formed by the R\(_{ΔR}\) values in different centrality bins and the values in the 40–80% centrality bin are presented.
We present a comprehensive theoretical study of the static spin response in HgTe quantum wells, revealing distinctive behavior for the topologically nontrivial inverted structure. Most strikingly, the q=0 (long-wavelength) spin susceptibility of the undoped topological-insulator system is constant and equal to the value found for the gapless Dirac-like structure, whereas the same quantity shows the typical decrease with increasing band gap in the normal-insulator regime. We discuss ramifications for the ordering of localized magnetic moments present in the quantum well, both in the insulating and electron-doped situations. The spin response of edge states is also considered, and we extract effective Landé g factors for the bulk and edge electrons. The variety of counterintuitive spin-response properties revealed in our study arises from the system’s versatility in accessing situations where the charge-carrier dynamics can be governed by ordinary Schrödinger-type physics; it mimics the behavior of chiral Dirac fermions or reflects the material’s symmetry-protected topological order.
Killing the cMSSM softly
(2016)
We investigate the constrained Minimal Supersymmetric Standard Model (cMSSM) in the light of constraining experimental and observational data from precision measurements, astrophysics, direct supersymmetry searches at the LHC and measurements of the properties of the Higgs boson, by means of a global fit using the program Fittino. As in previous studies, we find rather poor agreement of the best fit point with the global data. We also investigate the stability of the electro-weak vacuum in the preferred region of parameter space around the best fit point. We find that the vacuum is metastable, with a lifetime significantly longer than the age of the Universe. For the first time in a global fit of supersymmetry, we employ a consistent methodology to evaluate the goodness-of-fit of the cMSSM in a frequentist approach by deriving p values from large sets of toy experiments. We analyse analytically and quantitatively the impact of the choice of the observable set on the p value, and in particular its dilution when confronting the model with a large number of barely constraining measurements. Finally, for the preferred sets of observables, we obtain p values for the cMSSM below 10 %, i.e. we exclude the cMSSM as a model at the 90 % confidence level.
The main objectives of the KM3NeT Collaboration are (i) the discovery and subsequent observation of high-energy neutrino sources in the Universe and (ii) the determination of the mass hierarchy of neutrinos. These objectives are strongly motivated by two recent important discoveries, namely: (1) the high-energy astrophysical neutrino signal reported by IceCube and (2) the sizable contribution of electron neutrinos to the third neutrino mass eigenstate as reported by Daya Bay, Reno and others. To meet these objectives, the KM3NeT Collaboration plans to build a new Research Infrastructure consisting of a network of deep-sea neutrino telescopes in the Mediterranean Sea. A phased and distributed implementation is pursued which maximises the access to regional funds, the availability of human resources and the synergistic opportunities for the Earth and sea sciences community. Three suitable deep-sea sites are selected, namely off-shore Toulon (France), Capo Passero (Sicily, Italy) and Pylos (Peloponnese, Greece). The infrastructure will consist of three so-called building blocks. A building block comprises 115 strings, each string comprises 18 optical modules and each optical module comprises 31 photo-multiplier tubes. Each building block thus constitutes a three-dimensional array of photo sensors that can be used to detect the Cherenkov light produced by relativistic particles emerging from neutrino interactions. Two building blocks will be sparsely configured to fully explore the IceCube signal with similar instrumented volume, different methodology, improved resolution and
A search for Secluded Dark Matter annihilation in the Sun using 2007-2012 data of the ANTARES neutrino telescope is presented. Three different cases are considered: a) detection of dimuons that result from the decay of the mediator, or neutrino detection from: b) mediator that decays into a dimuon and, in turn, into neutrinos, and c) mediator that decays directly into neutrinos. As no significant excess over background is observed, constraints are derived on the dark matter mass and the lifetime of the mediator.
It has been proposed that the observed diphoton excess at 750 GeV could be explained within the constrained minimal supersymmetric standard model via resonantly produced stop bound states. We reanalyze this scenario critically and extend previous work to include the constraints from the stability of the electroweak vacuum and from the decays of the stoponium into a pair of Higgs bosons. It is shown that the interesting regions of parameter space with a light stop and Higgs of the desired mass are ruled out by these constraints. This conclusion is not affected by the presence of the bound states because the binding energy is usually very small in the regions of parameter space which can explain the Higgs mass. Thus, this also leads to strong constraints on the diphoton production cross section which is in general too small.
We present a supersymmetric left-right model which predicts gauge coupling unification close to the string scale and extra vector bosons at the TeV scale. The subtleties in constructing a model which is in agreement with the measured quark masses and mixing for such a low left-right breaking scale are discussed. It is shown that in the constrained version of this model radiative breaking of the gauge symmetries is possible and a SM-like Higgs is obtained. Additional CP-even scalars of a similar mass or even much lighter are possible. The expected mass hierarchies for the supersymmetric states differ clearly from those of the constrained MSSM. In particular, the lightest down-type squark, which is a mixture of the sbottom and extra vector-like states, is always lighter than the stop. We also comment on the model’s capability to explain current anomalies observed at the LHC.
Phase coexistence phenomena have been intensively studied in strongly correlated materials where several ordered states simultaneously occur or compete. Material properties critically depend on external parameters and boundary conditions, where tiny changes result in qualitatively different ground states. However, up to date, phase coexistence phenomena have exclusively been reported for complex compounds composed of multiple elements. Here we show that charge- and magnetically ordered states coexist in double-layer Fe/Rh(001). Scanning tunnelling microscopy and spectroscopy measurements reveal periodic charge-order stripes below a temperature of 130 K. Close to liquid helium temperature, they are superimposed by ferromagnetic domains as observed by spin-polarized scanning tunnelling microscopy. Temperature-dependent measurements reveal a pronounced cross-talk between charge and spin order at the ferromagnetic ordering temperature about 70 K, which is successfully modelled within an effective Ginzburg–Landau ansatz including sixth-order terms. Our results show that subtle balance between structural modifications can lead to competing ordering phenomena.
Active galactic nuclei (AGNs) are among the brightest sources in our universe. These galaxies are considered active because their central region is brighter than the luminosities of all stars in a galxies can provide. In their center is a supermassive black hole (SMBH) surrounded by an accretion disk and further out a dusty torus. AGN can be found with emission over the whole electromagnetic spectrum, starting at radio frequencies over optical and X-ray emission up to the $\gamma$-rays. Not all of these sources are detected in each frequency regime. In this work mainly blazars are examined at low radio frequencies. Blazars are a subclass of radio-loud AGN. These radio-loud sources usually exhibit highly collimated jets perpendicular to the accretion disk. For blazars these jets are pointed in the direction of the observer and their emission is highly variable. \\
AGN are classified in different subclasses based on their morphology. These different subclasses are combined in the AGN unification model, which explains the different morphologies by having sources only varying in their luminosities and their angle to the line of sight to the observer. Blazars are these targets, where the jet is pointing towards the observer, while the AGN observed edge on are called radio galaxies. This means that blazars should be the counterparts to radio galaxies seen from a different angle. Testing this is one of the goals in this work. \\
After the discovery of AGN in the 1940s these objects have been studied at all wavelengths. With the development of interferometry with radio telescopes the angular resolution for radio observations could be improved. In the last 20 years many AGN are regularly monitored. One of these monitoring programs is the MOJAVE program, monitoring 274 AGNs with using the Very Long Baseline Interferometry (VLBI) technique. The monitoring provides information on the evolution and structure of AGN and their jets. However, the mechanisms of the jet formation and their collimation are not fully understood. Due to relativistic effects it is difficult to obtain intrinsic instead of apparent parameters of these jets. One approach to get closer to the intrinsic jet power is by observing the regions, in which the jets end and interact with the intergalactic medium. Observations at lower radio frequencies are more sensitive for extended diffuse emission. \\
Since December 2012 a new radio telescope for low frequencies is observing. It is a telescope with stations consisting of dipole antennas. The major part of the array located in the Netherlands (38 stations) with 12 additional international stations in Germany, France, Sweden, Poland and the United Kingdom. This instrument is called the Low Frequency Array (LOFAR). LOFAR offers the possibility to observe at frequencies between 30--250 MHz in combination with angular resolution (below 1 arcsec for the full array), which was not available with previous telescopes. \\
In this work results of blazar studies with LOFAR observations are presented. To take advantage of a large database with multi-wavelength observations and kinematic studies the MOJAVE 1.5 Jy flux limited sample was chosen. Based on the preliminary results of the LOFAR Multifrequency Snapshot Sky Survey (MSSS) the flux densities and spectral indices of blazars of the MOJAVE sample are examined. 125 counterparts of MOJAVE blazars were found in the MSSS catalog. Since the MSSS observations only contain the stations in the Netherlands and observes in snapshots, the angular resolution and the sensitivity is limited. The first MSSS catalog was produced with an angular resolution of $\sim$120 arcsec and a sensitivity of $\sim$50--100 mJy. Another advantage of the MOJAVE sample is the monitoring of these sources with the Owens Valley Radio Observatory (OVRO) at 15 GHz to produce radio lightcurves. With these observations it is possible to get quasi-simultaneous flux densities at 15 GHz for the corresponding MSSS observations. By having quasi-simultaneous observations the variability of the blazars affects the flux densities less than with the use of archival data. The spectral indices obtained by the combination of MSSS and OVRO flux densities can be used to estimate the contribution of the diffuse extended emission for these AGNs. \\
Comparing the MSSS catalog with the OVRO data points, the flux densities have a tendency to be higher at low frequencies. This is expected due to the higher contribution of extended emission. The broadband spectral index distribution shows a peak at $\sim-0.2$. While some sources seem to have steeper spectral indices meaning that extended emission contributes a large fraction of the total flux density, more than the half of the sample shows flat spectral indices. The flat spectral indices show that the total flux densities of these sources are dominated by their relativistic beamed emission regions, which is the same for the observations at GHz frequencies. \\
To obtain more detailed images of these sources the MSSS measurement sets including sources of the sample were reprocessed to improve the angular resolution to $\sim$30 arcsec. The higher angular resolution reveals extended diffuse emission of several blazars. Since the reimaging results were not fully calibrated only the morphology at this resolution could be examined. However, with the short snapshot observations the images obtained with this strategy are affected from artifacts. The reimaging could be successfully performed for 93 sources in one frequency band. For 45 of these sources all availabe frequency bands could be reprocessed and used to created averaged images. These images are presented in this work. As a results of the reimaging process a pilot sample was defined to observe targets with diffuse extended emission using the whole LOFAR array including the international stations. \\
The second part of this work presents the results of a pilot sample consisting of four blazars observed with the LOFAR international array. Since the calibration of this kind of LOFAR observation is still in development, the main focus was the description of the used calibration strategy. The calibration strategies still has some limitation but resulted in images with angular resolutions of less than 1 arcsec. The morphology of all four blazars show features confirming the expectations of their counterpart radio galaxies. With the flux densities of the extended emission found in these brightness distributions the extended radio luminosities are calculated. Comparing these to the radio galaxy classifications also confirm the expectations from the unification model. \\
By extending the sample of observed blazars with LOFAR international in future the calibration strategy can be used to create similar high resolution images. A larger sample can be used to test the unification model with statistical significant results. \\
The most energetic versions of active galactic nuclei (AGNs) feature two highly-relativistic plasma outflows, so-called jets, that are created in the vicinity of the central supermassive black hole and evolve in opposite directions. In blazars, which dominate the extragalactic gamma-ray sky, the jets are aligned close to the observer's line of sight leading to strong relativistic beaming effects of the jet emission. Radio observations especially using very long baseline interferometry (VLBI) provide the best way to gain direct information on the intrinsic properties of jets down to sub-parsec scales, close to their formation region.
In this thesis, I focus on the properties of three AGNs, IC 310, PKS 2004-447, and 3C 111 that belong to the small non-blazar population of gamma-ray-loud AGNs. In these kinds of AGNs, the jets are less strongly aligned with respect to the observer than in blazars. I study them in detail with a variety of radio astronomical instruments with respect to their high-energy emission and in the context of the large samples in the monitoring programmes MOJAVE and TANAMI. My analysis of radio interferometric observations and flux density monitoring data reveal very different characteristics of the jet emission in these sources. The work presented in this thesis illustrates the diversity of the radio properties of gamma-ray-loud AGNs that do not belong to the dominating class of blazars.
At a hadron collider as the LHC or the Tevatron the production of a photon in association with a leptonically decaying vector boson represents an important class of processes. These processes stand out due to a very clean signal of a photon and two leptons. Furthermore they
provide direct access to the photon–vector-boson couplings and thus an easy opportunity to test the
gauge sector of the Standard Model. Within the scope of this work we present a full calculation of the next-to-leading-order corrections which include the O (αs) corrections of the strong interaction as well as the electroweak corrections of O (α) including all photon-induced contributions. For the creation of matrix elements we use methods based on Feynman diagrams. The IR singularities are treated with the dipole subtraction technique. In order to separate photons from jets, a quark-to-photon fragmentation function ´a la Glover / Morgan or Frixione’s cone isolation is employed. Moreover, two different scenarios for charged leptons in the fi state were considered. The fi scenario for dressed leptons assumes that a charged lepton and a photon will be recombined if they are collinear. In the second scenario for bare muons it is assumed that leptons and photon can be separated in a detector also if they are collinear.
For our calculation we implemented all corrections into a fl Monte Carlo program. Be- sides the computation of the total cross section this program is also able to generate diff tial distributions of several experimentally motivated observables. Apart from the expected large electroweak corrections in the high transverse-momentum regions and sizeable corrections in the resonance regions of the transverse or the invariant masses we found photon-induced corrections up to several 10% for high transverse momenta. Within run I at the LHC for 7/8 TeV the experimental accuracy for Vγ production was roughly 10%. Due to the higher luminosity at run II this accuracy
will be reduced to the level of a few percent so that corrections of the same order within the theoretical predictions might become relevant. In this work we present results for the total cross section at the LHC for 7, 8 and 14 TeV and the corresponding distributions
for 14 TeV.
Due to their potential application for quantum computation, quantum dots have attracted a lot of interest in recent years. In these devices single electrons can be captured, whose spin can be used to define a quantum bit (qubit). However, the information stored in these quantum bits is fragile due to the interaction of the electron spin with its environment. While many of the resulting problems have already been solved, even on the experimental side, the hyperfine interaction between the nuclear spins of the host material and the electron spin in their center remains as one of the major obstacles. As a consequence, the reduction of the number of nuclear spins is a promising way to minimize this effect. However, most quantum dots have a fixed number of nuclear spins due to the presence of group III and V elements of the periodic table in the host material. In contrast, group IV elements such as carbon allow for a variable size of the nuclear spin environment through isotopic purification. Motivated by this possibility, we theoretically investigate the physics of the central spin model in carbon based quantum dots. In particular, we focus on the consequences of a variable number of nuclear spins on the decoherence of the electron spin in graphene quantum dots.
Since our models are, in many aspects, based upon actual experimental setups, we provide an overview of the most important achievements of spin qubits in quantum dots in the first part of this Thesis. To this end, we discuss the spin interactions in semiconductors on a rather general ground. Subsequently, we elaborate on their effect in GaAs and graphene, which can be considered as prototype materials. Moreover, we also explain how the central spin model can be described in terms of open and closed quantum systems and which theoretical tools are suited to analyze such models.
Based on these prerequisites, we then investigate the physics of the electron spin using analytical and numerical methods. We find an intriguing thermal flip of the electron spin using standard statistical physics. Subsequently, we analyze the dynamics of the electron spin under influence of a variable number of nuclear spins. The limit of a large nuclear spin environment is investigated using the Nakajima-Zwanzig quantum master equation, which reveals a decoherence of the electron spin with a power-law decay on short timescales. Interestingly, we find a dependence of the details of this decay on the orientation of an external magnetic field with respect to the graphene plane. By restricting to a small number of nuclear spins, we are able to analyze the dynamics of the electron spin by exact diagonalization, which provides us with more insight into the microscopic details of the decoherence. In particular, we find a fast initial decay of the electron spin, which asymptotically reaches a regime governed by small fluctuations around a finite long-time average value. Finally, we analytically predict upper bounds on the size of these fluctuations in the framework of quantum thermodynamics.
Classical novae are thermonuclear explosions occurring on the surface of white dwarfs.
When co-existing in a binary system with a main sequence or more evolved star, mass
accretion from the companion star to the white dwarf can take place if the companion
overflows its Roche lobe. The envelope of hydrogen-rich matter which builds on
top of the white dwarf eventually ignites under degenerate conditions, leading to
a thermonuclear runaway and an explosion in the order of 1046 erg, while leaving
the white dwarf intact. Spectral analyses from the debris indicate an abundance of
isotopes that are tracers of nuclear burning via the hot CNO cycle, which in turn
reveal some sort of mixing between the envelope and the white dwarf underneath.
The exact mechanism is still a matter of debate.
The convection and deflagration in novae develop in the low Mach number regime.
We used the Seven League Hydro code (SLH ), which employs numerical schemes
designed to correctly simulate low Mach number flows, to perform two and three-
dimensional simulations of classical novae. Based on a spherically-symmetric model
created with aid of a stellar evolution code, we developed our own nova model and
tested it on a variety of numerical grids and boundary conditions for validation. We
focused on the evolution of temperature, density and nuclear energy generation rate at
the layers between white dwarf and envelope, where most of the energy is generated,
to understand the structure of the transition region, and its effect on the nuclear
burning. We analyzed the resulting dredge-up efficiency stemming from the convective
motions in the envelope. Our models yield similar results to the literature, but seem
to depend very strongly on the numerical resolution. We followed the evolution of
the nuclear species involved in the CNO cycle and concluded that the thermonuclear
reactions primarily taking place are those of the cold and not the hot CNO cycle.
The reason behind this could be that under the conditions generally assumed for
multi-dimensional simulations, the envelope is in fact not degenerate. We performed
initial tests for 3D simulations and realized that alternative boundary conditions are
needed.
A prototype detection unit of the KM3NeT deep-sea neutrino telescope has been installed at 3500m depth 80 km offshore the Italian coast. KM3NeT in its final configuration will contain several hundreds of detection units. Each detection unit is a mechanical structure anchored to the sea floor, held vertical by a submerged buoy and supporting optical modules for the detection of Cherenkov light emitted by charged secondary particles emerging from neutrino interactions. This prototype string implements three optical modules with 31 photomultiplier tubes each. These optical modules were developed by the KM3NeT Collaboration to enhance the detection capability of neutrino interactions. The prototype detection unit was operated since its deployment in May 2014 until its decommissioning in July 2015. Reconstruction of the particle trajectories from the data requires a nanosecond accuracy in the time calibration. A procedure for relative time calibration of the photomultiplier tubes contained in each optical module is described. This procedure is based on the measured coincidences produced in the sea by the 40K background light and can easily be expanded to a detector with several thousands of optical modules. The time offsets between the different optical modules are obtained using LED nanobeacons mounted inside them. A set of data corresponding to 600 h of livetime was analysed. The results show good agreement with Monte Carlo simulations of the expected optical background and the signal from atmospheric muons. An almost background-free sample of muons was selected by filtering the time correlated signals on all the three optical modules. The zenith angle of the selected muons was reconstructed with a precision of about 3∘.
Next-to-leading-order electroweak corrections to pp -> W\(^{+}\)W\(^{-}\) -> 4 leptons at the LHC
(2016)
We present results of the first calculation of next-to-leading-order electroweak corrections to W-boson pair production at the LHC that fully takes into account leptonic W-boson decays and off-shell effects. Employing realistic event selections, we discuss the corrections in situations that are typical for the study of W-boson pairs as a signal process or of Higgs-boson decays H → WW∗, to which W-boson pair production represents an irreducible background. In particular, we compare the full off-shell results, obtained treating the W-boson resonances in the complex-mass scheme, to previous results in the so-called double-pole approximation, which is based on an expansion of the loop amplitudes about the W resonance poles. At small and intermediate scales, i.e. in particular in angular and rapidity distributions, the two approaches show the expected agreement at the level of fractions of a percent, but larger differences appear in the TeV range. For transverse-momentum distributions, the differences can even exceed the 10% level in the TeV range where “background diagrams” with one instead of two resonant W bosons gain in importance because of recoil effects.
A search for muon neutrinos originating from dark matter annihilations in the Sun is performed using the data recorded by the ANTARES neutrino telescope from 2007 to 2012. In order to obtain the best possible sensitivities to dark matter signals, an optimisation of the event selection criteria is performed taking into account the background of atmospheric muons, atmospheric neutrinos and the energy spectra of the expected neutrino signals. No significant excess over the background is observed and 90% C.L. upper limits on the neutrino flux, the spin-dependent and spin-independent WIMP-nucleon cross-sections are derived for WIMP masses ranging from 50 GeV to 5 TeV for the annihilation channels WIMP + WIMP→ b\(\overline{b}\), W\(^{+}\)W\(^{−}\) and τ\(^{+}\)τ\(^{−}\).
A highly significant excess of high-energy astrophysical neutrinos has been reported by the IceCube Collaboration. Some features of the energy and declination distributions of IceCube events hint at a North/South asymmetry of the neutrino flux. This could be due to the presence of the bulk of our Galaxy in the Southern hemisphere. The ANTARES neutrino telescope, located in the Mediterranean Sea, has been taking data since 2007. It offers the best sensitivity to muon neutrinos produced by galactic cosmic ray interactions in this region of the sky. In this letter a search for an extended neutrino flux from the Galactic Ridge region is presented. Different models of neutrino production by cosmic ray propagation are tested. No excess of events is observed and upper limits for different neutrino flux spectral indices Γ are set. For Γ=2.4 the 90% confidence level flux upper limit at 100 TeV for one neutrino flavour corresponds to Φ\(^{1f}_{0}\) (100 TeV) = 2.0 · 10\(^{−17}\) GeV\(^{−1}\) cm\(^{−2}\)s\(^{−1}\)sr\(^{−1}\). Under this assumption, at most two events of the IceCube cosmic candidates can originate from the Galactic Ridge. A simple power-law extrapolation of the Fermi-LAT flux to account for IceCube High Energy Starting Events is excluded at 90% confidence level.
The next-to-leading-order electroweak corrections to pp→l\(^{+}\)l\(^{-}\)/ν¯¯¯ν+γ+X production, including all off-shell effects of intermediate Z bosons in the complex-mass scheme, are calculated for LHC energies, revealing the typically expected large corrections of tens of percent in the TeV range. Contributions from quark-photon and photon-photon initial states are taken into account as well, but their impact is found to be moderate or small. Moreover, the known next-to-leading-order QCD corrections are reproduced. In order to separate hard photons from jets, both a quark-to-photon fragmentation function á la Glover/Morgan and Frixione’s cone isolation are employed. The calculation is available in the form of Monte Carlo programs allowing for the evaluation of arbitrary differential cross sections. Predictions for integrated cross sections are presented for the LHC at 7 TeV, 8 TeV, and 14 TeV, and differential distributions are discussed at 14 TeV for bare muons and dressed leptons. Finally, we consider the impact of anomalous ZZγ and Zγγ couplings.
NLO electroweak corrections to off-shell top-antitop production with leptonic decays at the LHC
(2016)
For the first time the next-to-leading-order electroweak corrections to the full off-shell production of two top quarks that decay leptonically are presented. This calculation includes all off-shell, non-resonant, and interference effects for the 6-particle phase space. While the electroweak corrections are below one per cent for the integrated cross section, they reach up to 15% in the high-transverse-momentum region of distributions. To support the results of the complete one-loop calculation, we have in addition evaluated the electroweak corrections in two different pole approximations, one requiring two on-shell top quarks and one featuring two on-shell W bosons. While the former deviates by up to 10% from the full calculation for certain distributions, the latter provides a very good description for most observables. The increased centre-of-mass energy of the LHC makes the inclusion of electroweak corrections extremely relevant as they are particularly large in the Sudakov regime where new physics is expected to be probed.
We present evidence for the existence of a hybrid state of Tamm plasmons and microcavity exciton polaritons in a II-VI material based microcavity sample covered with an Ag metal layer. The bare cavity mode shows a characteristic anticrossing with the Tamm-plasmon mode, when microreflectivity measurements are performed for different detunings between the Tamm plasmon and the cavity mode. When the Tamm-plasmon mode is in resonance with the cavity polariton four hybrid eigenstates are observed due to the coupling of the cavity-photon mode, the Tamm-plasmon mode, and the heavy- and light-hole excitons. If the bare Tamm-plasmon mode is tuned, these resonances will exhibit three anticrossings. Experimental results are in good agreement with calculations based on the transfer matrix method as well as on the coupled-oscillators model. The lowest hybrid eigenstate is observed to be red shifted by about 13 meV with respect to the lower cavity polariton state when the Tamm plasmon is resonantly coupled with the cavity polariton. This spectral shift which is caused by the metal layer can be used to create a trapping potential channel for the polaritons. Such channels can guide the polariton propagation similar to one-dimensional polariton wires.
We present a consistent renormalization scheme for the CP-conserving Two-Higgs-Doublet Model based on (MS)over-bar renormalization of the mixing angles and the soft-Z 2-symmetry-breaking scale M sb in the Higgs sector. This scheme requires to treat tadpoles fully consistently in all steps of the calculation in order to provide gauge-independent S-matrix elements. We show how bare physical parameters have to be defined and verify the gauge independence of physical quantities by explicit calculations in a general R ξ -gauge. The procedure is straightforward and applicable to other models with extended Higgs sectors. In contrast to the proposed scheme, the (MS)over-bar renormalization of the mixing angles combined with popular on-shell renormalization schemes gives rise to gauge-dependent results already at the one-loop level. We present explicit results for electroweak NLO corrections to selected processes in the appropriately renormalized Two-Higgs-Doublet Model and in particular discuss their scale dependence.
Entropy production in industrial economies involves heat currents, driven by gradients of temperature, and particle currents, driven by specific external forces and gradients of temperature and chemical potentials. Pollution functions are constructed for the associated emissions. They reduce the output elasticities of the production factors capital, labor, and energy in the growth equation of the capital-labor-energy-creativity model, when the emissions approach their critical limits. These are drawn by, e.g., health hazards or threats to ecological and climate stability. By definition, the limits oblige the economic actors to dedicate shares of the available production factors to emission mitigation, or to adjustments to the emission-induced changes in the biosphere. Since these shares are missing for the production of the quantity of goods and services that would be available to consumers and investors without emission mitigation, the “conventional” output of the economy shrinks. The resulting losses of conventional output are estimated for two classes of scenarios: (1) energy conservation; and (2) nuclear exit and subsidies to photovoltaics. The data of the scenarios refer to Germany in the 1980s and after 11 March 2011. For the energy-conservation scenarios, a method of computing the reduction of output elasticities by emission abatement is proposed.
The prediction and the experimental discovery of topological insulators has set the stage for a novel type of electronic devices. In contrast to conventional metals or semiconductors, this new class of materials exhibits peculiar transport properties at the sample surface, as conduction channels emerge at the topological boundaries of the system.
In specific materials with strong spin-orbit coupling, a particular form of a two-dimensional topological insulator, the quantum spin Hall state, can be observed.
Here, the respective one-dimensional edge channels are helical in nature, meaning that there is a locking of the spin orientation of an electron and its direction of motion.
Due to the symmetry of time-reversal, elastic backscattering off interspersed impurities is suppressed in such a helical system, and transport is approximately ballistic.
This allows in principle for the realization of novel energy-efficient devices, ``spintronic`` applications, or the formation of exotic bound states with non-Abelian statistics, which could be used for quantum computing.
The present work is concerned with the general transport properties of one-dimensional helical states. Beyond the topological protection mentioned above, inelastic backscattering can arise from various microscopic sources, of which the most prominent ones will be discussed in this Thesis. As it is characteristic for one-dimensional systems, the role of electron-electron interactions can be of major importance in this context.
First, we review well-established techniques of many-body physics in one dimension such as perturbative renormalization group analysis, (Abelian) bosonization, and Luttinger liquid theory. The latter allow us to treat electron interactions in an exact way.
Those methods then are employed to derive the corrections to the conductance in a helical transport channel, that arise from various types of perturbations.
Particularly, we focus on the interplay of Rashba spin-orbit coupling and electron interactions as a source of inelastic single-particle and two-particle backscattering. It is demonstrated, that microscopic details of the system, such as the existence of a momentum cutoff, that restricts the energy spectrum, or the presence of non-interacting leads attached to the system, can fundamentally alter the transport signature.
By comparison of the predicted corrections to the conductance to a transport experiment, one can gain insight about the microscopic processes and the structure of a quantum spin Hall sample.
Another important mechanism we analyze is backscattering induced by magnetic moments. Those findings provide an alternative interpretation of recent transport measurements in InAs/GaSb quantum wells.
Within gauge/gravity duality, we consider the local quench-like time evolution obtained by joining two 1+1-dimensional heat baths at different temperatures at time \(t\) = 0. A steady state forms and expands in space. For the 2+1-dimensional gravity dual, we find that the “shockwaves” expanding the steady-state region are of spacelike nature in the bulk despite being null at the boundary. However, they do not transport information. Moreover, by adapting the time-dependent Hubeny-Rangamani-Takayanagi prescription, we holographically calculate the entanglement entropy and also the mutual information for different entangling regions. For general temperatures, we find that the entanglement entropy increase rate satisfies the same bound as in the ‘entanglement tsunami’ setups. For small temperatures of the two baths, we derive an analytical formula for the time dependence of the entanglement entropy. This replaces the entanglement tsunami-like behaviour seen for high temperatures. Finally, we check that strong subadditivity holds in this time-dependent system, as well as further more general entanglement inequalities for five or more regions recently derived for the static case.
Blazars like Markarian 421 or Markarian 501 are active galactic nuclei (AGN), with their jets orientated towards the observer. They are among the brightest objects in the very high energy (VHE) gamma ray regime (>100 GeV). Their emitted gamma-ray fluxes are extremely variable, with changing activity levels on timescales between minutes, months, and even years. Several questions are part of the current research, such as the question of the emission regions or the engine of the AGN and the particle acceleration. A dedicated longterm monitoring program is necessary to investigate the properties of blazars in detail. A densely sampled and unbiased light curve allows for observation of both high and low states of the sources, and the combination with multi-wavelength observation could contribute to the answer of several questions mentioned above. FACT (First G-APD Cherenkov Telescope) is the first operational telescope using silicon photomultiplier (SiPM, also known as Geigermode—Avalanche Photo Diode, G-APD) as photon detectors. SiPM have a very homogenous and stable longterm performance, and allow operation even during full moon without any filter, leading to a maximal duty cycle for an Imaging Air Cherenkov Telescope (IACT). Hence, FACT is an ideal device for such a longterm monitoring of bright blazars. A small set of sources (e.g., Markarian 421, Markarian 501, 1ES 1959+650, and 1ES 2344+51.4) is currently being monitored. In this contribution, the FACT telescope and the concept of longterm monitoring of bright blazars will be introduced. The results of the monitoring program will be shown, and the advantages of densely sampled and unbiased light curves will be discussed.
Chromium dioxide CrO\(_2\) belongs to a class of materials called ferromagnetic half-metals, whose peculiar aspect is that they act as a metal in one spin orientation and as a semiconductor or insulator in the opposite one. Despite numerous experimental and theoretical studies motivated by technologically important applications of this material in spintronics, its fundamental properties such as momentumresolved electron dispersions and the Fermi surface have so far remained experimentally inaccessible because of metastability of its surface, which instantly reduces to amorphous Cr\(_2\)O\(_3\). In this work, we demonstrate that direct access to the native electronic structure of CrO\(_2\) can be achieved with soft-x-ray angle-resolved photoemission spectroscopy whose large probing depth penetrates through the Cr\(_2\)O\(_3\) layer. For the first time, the electronic dispersions and Fermi surface of CrO\(_2\) are measured, which are fundamental prerequisites to solve the long debate on the nature of electronic correlations in this material. Since density functional theory augmented by a relatively weak local Coulomb repulsion gives an exhaustive description of our spectroscopic data, we rule out strong-coupling theories of CrO\(_2\). Crucial for the correct interpretation of our experimental data in terms of the valence-band dispersions is the understanding of a nontrivial spectral response of CrO\(_2\) caused by interference effects in the photoemission process originating from the nonsymmorphic space group of the rutile crystal structure of CrO\(_2\).
We calculate the next-to-leading order electroweak corrections to the production of a photon pair in association with zero, one and two jets at the LHC. We use GoSam and Sherpa to obtain the results in a fully automated way. For a typical set of fiducial cuts the electroweak corrections lead to a modification of the total cross section of up to 3%, depending on the jet multiplicity. We find substantial contributions in differential distributions, leading to tens of per cent corrections for phase space regions within the reach of the LHC. Furthermore we investigate the importance of photon induced processes as well as subleading contributions. Photon induced processes are found to be negligible, subleading contributions can have a sizeable impact however they can be removed by appropriate phase space cuts.
Higgs production in association with off-shell top-antitop pairs at NLO EW and QCD at the LHC
(2017)
We present NLO electroweak corrections to Higgs production in association with off-shell top-antitop quark pairs. The full process pp → e +νeµ −ν¯µbb¯H is considered, and hence all interference, off-shell, and non-resonant contributions are taken into account.
The electroweak corrections turn out to be below one per cent for the integrated cross section but can exceed 10% in certain phase-space regions. In addition to its phenomenological relevance, the computation constitutes a major technical achievement as the full NLO virtual corrections involving up to 9-point functions have been computed exactly. The results of the full computation are supported by two calculations in the double-pole approximation. These also allow to infer the effect of off-shell contributions and emphasise their importance especially for the run II of the LHC. Finally, we present combined predictions featuring both NLO electroweak and QCD corrections in a common set-up that will help the experimental collaborations in their quest of precisely measuring the aforementioned process.
High-energy jets recoiling against missing transverse energy (MET) are powerful probes of dark matter at the LHC. Searches based on large MET signatures require a precise control of the \({Z(ν\overline{ν})}+\) jet background in the signal region. This can be achieved by taking accurate data in control regions dominated by \(Z(ℓ^+ℓ^−)+\) jet, \(W(ℓν)+\) jet and \(γ+\) jet production, and extrapolating to the \({Z(ν\overline{ν})}+\) jet background by means of precise theoretical predictions. In this context, recent advances in perturbative calculations open the door to significant sensitivity improvements in dark matter searches. In this spirit, we present a combination of state-of-the-art calculations for all relevant \(V+\) jets processes, including throughout NNLO QCD corrections and NLO electroweak corrections supplemented by Sudakov logarithms at two loops. Predictions at parton level are provided together with detailed recommendations for their usage in experimental analyses based on the reweighting of Monte Carlo samples. Particular attention is devoted to the estimate of theoretical uncertainties in the framework of dark matter searches, where subtle aspects such as correlations across different \(V+\) jet processes play a key role. The anticipated theoretical uncertainty in the \({Z(ν\overline{ν})}+\) jet background is at the few percent level up to the TeV range.
Next-to-leading-order electroweak corrections to the production of four charged leptons at the LHC
(2017)
We present a state-of-the-art calculation of the next-to leading-order electroweak corrections to ZZ production, including the leptonic decays of the Z bosons into μ\(^+\)μ\(^ −\)e\(^+\)e\(^−\) or μ\(^+\)μ\(^−\)μ\(^+\)μ\(^−\) final states. We use complete leading-order and next-to-leading-order matrix elements for four-lepton production, including contributions of virtual photons and all off-shell effects of Z bosons, where the finite Z-boson width is taken into account using the complex-mass scheme. The matrix elements are implemented into Monte Carlo programs allowing for the evaluation of arbitrary differential distributions. We present integrated and differential cross sections for the LHC at 13 TeV both for an inclusive setup where only lepton identification cuts are applied, and for a setup motivated by Higgs-boson analyses in the four-lepton decay channel. The electroweak corrections are divided into photonic and purely weak contributions. The former show the well-known pronounced tails near kinematical thresholds and resonances; the latter are generically at the level of ∼ −5% and reach several −10% in the high-energy tails of distributions. Comparing the results for μ\(^+\)μ\(^−\)e\(^+\)e\(^−\) and μ\(^+\)μ\(^−\)μ\(^+\)μ\(^−\) final states, we find significant differences mainly in distributions that are sensitive to the μ\(^+\)μ\(^−\) pairing in the μ\(^+\)μ\(^−\)μ\(^+\)μ\(^−\) final state. Differences between μ\(^+\)μ\(^−\)e\(^+\)e\(^−\) and μ\(^+\)μ\(^−\)μ\(^+\)μ\(^−\) channels due to interferences of equal-flavour leptons in the final state can reach up to 10% in off-shell-sensitive regions. Contributions induced by incoming photons, i.e. photon-photon and quark-photon channels, are included, but turn out to be phenomenologically unimportant.
Advanced LIGO detected a significant gravitational wave signal (GW170104) originating from the coalescence of two black holes during the second observation run on January 4th, 2017. An all-sky high-energy neutrino follow-up search has been made using data from the Antares neutrino telescope, including both upgoing and downgoing events in two separate analyses. No neutrino candidates were found within ±500 s around the GW event time nor any time clustering of events over an extended time window of ±3 months. The non-detection is used to constrain isotropic-equivalent high-energy neutrino emission from GW170104 to less than ∼ 1.2 × \(10^{55}\) erg for a \(E^{−2}\) spectrum. This constraint is valid in the energy range corresponding to the 5–95% quantiles of the neutrino flux [3.2 TeV; 3.6 PeV], if the GW emitter was below the Antares horizon at the alert time.
We consider a scenario inspired by natural supersymmetry, where neutrino data is explained within a low-scale seesaw scenario. We extend the Minimal Supersymmetric Standard Model by adding light right-handed neutrinos and their superpartners, the R-sneutrinos, and consider the lightest neutralinos to be higgsino-like. We consider the possibilities of having either an R-sneutrino or a higgsino as lightest supersymmetric particle. Assuming that squarks and gauginos are heavy, we systematically evaluate the bounds on slepton masses due to existing LHC data.
The topic of this PhD thesis is the combination of topologically non-trivial phases with correlation effects stemming from Coulomb interaction between the electrons in a condensed matter system. Emphasis is put on both emerging benefits as well as hindrances, e.g. concerning the topological protection in the presence of strong interactions.
The physics related to topological effects is established in Sec. 2. Based on the topological band theory, we introduce topological materials including Chern insulators, topological insulators in two and three dimensions as well as Weyl semimetals. Formalisms for a controlled treatment of Coulomb correlations are presented in Sec. 3, starting with the topological field theory. The Random Phase Approximation is introduced as a perturbative approach, while in the strongly interacting limit the theory of quantum Hall ferromagnetism applies. Interactions in one dimension are special, and are treated through the Luttinger liquid description. The section ends with an overview of the expected benefits offered by the combination of topology and interactions, see Sec. 3.3.
These ideas are then elaborated in the research part. In Chap. II, we consider weakly interacting 2D topological insulators, described by the Bernevig-Hughes-Zhang model. This is applicable, e.g., to quantum well structures made of HgTe/CdTe or InAs/GaSb. The bulk band structure is here a mixture stemming from linear Dirac and quadratic Schrödinger fermions. We study the low-energy excitations in Random Phase Approximation, where a new interband plasmon emerges due to the combined Dirac and Schrödinger physics, which is absent in the separate limits. Already present in the undoped limit, one finds it also at finite doping, where it competes with the usual intraband plasmon. The broken particle-hole symmetry in HgTe quantum wells allows for an effective separation of the two in the excitation spectrum for experimentally accessible parameters, in the right range for Raman or electron loss spectroscopy. The interacting bulk excitation spectrum shows here clear differences between the topologically trivial and topologically non-trivial regime. An even stronger signal in experiments is expected from the optical conductivity of the system. It thus offers a quantitative way to identify the topological phase of 2D topological insulators from a bulk measurement.
In Chap. III, we study a strongly interacting system, forming an ordered, quantum Hall ferromagnetic state. The latter can arise also in weakly interacting materials with an applied strong magnetic field. Here, electrons form flat Landau levels, quenching the kinetic energy such that Coulomb interaction can be dominant. These systems define the class of quantum Hall topological insulators: topologically non-trivial states at finite magnetic field, where the counter-propagating edge states are protected by a symmetry (spatial or spin) other than time-reversal. Possible material realizations are 2D topological insulators like HgTe heterostructures and graphene. In our analysis, we focus on the vicinity of the topological phase transition, where the system is in a strongly interacting quantum Hall ferromagnetic state. The bulk and edge physics can be described by a nonlinear \sigma-model for the collective order parameter of the ordered state. We find that an emerging, continuous U(1) symmetry offers topological protection. If this U(1) symmetry is preserved, the topologically non-trivial phase persists in the presence of interactions, and we find a helical Luttinger liquid at the edge. The latter is highly tunable by the magnetic field, where the effective interaction strength varies from weakly interacting at zero field, K \approx 1, to diverging interaction strength at the phase transition, K -> 0.
In the last Chap. IV, we investigate whether a Weyl semimetal and a 3D topological insulator phase can exist together at the same time, with a combined, hybrid surface state at the joint boundaries. An overlap between the two can be realized by Coulomb interaction or a spatial band overlap of the two systems. A tunnel coupling approach allows us to derive the hybrid surface state Hamiltonian analytically, enabling a detailed study of its dispersion relation. For spin-symmetric coupling, new Dirac nodes emerge out of the combination of a single Dirac node and a Fermi arc. Breaking the spin symmetry through the coupling, the dispersion relation is gapped and the former Dirac node gets spin-polarized. We propose experimental realizations of the hybrid physics, including compressively strained HgTe as well as heterostructures of topological insulator and Weyl semimetal materials, connected to each other, e.g., by Coulomb interaction.
The thesis deals with the automated generation and efficient evaluation of scattering amplitudes in general relativistic quantum field theories at one-loop order in perturbation theory. At the
present time we lack signals beyond the Standard Model which, in the past, have guided the
high-energy physics community, and ultimately led to the discovery of new physics phenomena.
In the future, precision tests could acquire this guiding role by systematically probing the Standard Model and constraining Beyond the Standard Model theories. As current experimental
constraints strongly favour Standard Model-like theories, only small deviations with respect to the Standard Model are expected which need to be studied in detail. The required precision
demands one-loop corrections in all future analyses, ideally in a fully automated way, allowing
to test a variety of observables in different models and in an effective field theory approach.
In the process of achieving this goal we have developed an enhanced version of the tool
Recola and on this basis the generalization Recola2. These tools represent fully automated
tree- and one-loop-amplitude providers for the Standard Model, or in the case of Recola2
for general models. Concerning the algorithm, we use a purely numerical and fully recursive
approach allowing for extreme calculations of yet unmatched complexity. Recola has led to the first computation involving 9-point functions. Beyond the Standard Model theories and Effective Field theories are integrated into the Recola2 framework as model files. Renormalized model files are produced with the newly developed tool Rept1l, which can perform the renormalization in a fully automated way, starting from nothing but Feynman rules. In view of validation, we have extended Recola2 to new gauges such as the Background-Field Method and the class of Rxi gauges. In particular, the Background-Field Method formulation for new theories serves as an automated validation, and is very useful in practical calculations and the formulation of renormalization conditions. We have applied the system to produce the first results for Higgs-boson production in Higgs strahlung and vector-boson fusion in the Two-Higgs-Doublet Model and the Higgs-Singlet Extension of the Standard Model. All in all, we have laid the foundation for an automated generation and computation of one-loop amplitudes within a large class of phenomenologically interesting theories. Furthermore, we enable the use of our system via a very flexible and dynamic control which does not require any intermediate intervention.
Frequency analysis of the rf emission of oscillating Josephson supercurrent is a powerful passive way of probing properties of topological Josephson junctions. In particular, measurements of the Josephson emission enable the detection of topological gapless Andreev bound states that give rise to emission at half the Josephson frequency f\(_{J}\) rather than conventional emission at f\(_{J}\). Here, we report direct measurement of rf emission spectra on Josephson junctions made of HgTe-based gate-tunable topological weak links. The emission spectra exhibit a clear signal at half the Josephson frequency f\(_{J}\)/2. The linewidths of emission lines indicate a coherence time of 0.3–4 ns for the f\(_{J}\)/2 line, much shorter than for the f\(_{J}\) line (3–4 ns). These observations strongly point towards the presence of topological gapless Andreev bound states and pave the way for a future HgTe-based platform for topological quantum computation.
Just as photons are the quanta of light, plasmons are the quanta of orchestrated charge-density oscillations in conducting media. Plasmon phenomena in normal metals, superconductors, and doped semiconductors are often driven by long-wavelength Coulomb interactions. However, in crystals whose Fermi surface is comprised of disconnected pockets in the Brillouin zone, collective electron excitations can also attain a shortwave component when electrons transition between these pockets. In this work, we show that the band structure of monolayer transition-metal dichalcogenides gives rise to an intriguing mechanism through which shortwave plasmons are paired up with excitons. The coupling elucidates the origin for the optical sideband that is observed repeatedly in monolayers of WSe\(_2\) and WS\(_2\) but not understood. The theory makes it clear why exciton-plasmon coupling has the right conditions to manifest itself distinctly only in the optical spectra of electron-doped tungsten-based monolayers.
Low-energy spin excitations in any long-range ordered magnetic system in the absence of magnetocrystalline anisotropy are gapless Goldstone modes emanating from the ordering wave vectors. In helimagnets, these modes hybridize into the so-called helimagnon excitations. Here we employ neutron spectroscopy supported by theoretical calculations to investigate the magnetic excitation spectrum of the isotropic Heisenberg helimagnet \({ZnCr_2Se_4}\) with a cubic spinel structure, in which spin\(-3/2\) magnetic \({Cr^{3+}}\) ions are arranged in a geometrically frustrated pyrochlore sublattice. Apart from the conventional Goldstone mode emanating from the \((0~ 0~ {q_h})\) ordering vector, low-energy magnetic excitations in the single-domain proper-screw spiral phase show soft helimagnon modes with a small energy gap of \({∼0.17~ meV}\), emerging from two orthogonal wave vectors \(({q_h}~ 0~ 0)\) and \({(0~ {q_h}~ 0)}\) where no magnetic Bragg peaks are present. We term them pseudo-Goldstone magnons, as they appear gapless within linear spinwave theory and only acquire a finite gap due to higher-order quantum-fluctuation corrections. Our results are likely universal for a broad class of symmetric helimagnets, opening up a new way of studying weak magnon-magnon interactions with accessible spectroscopic methods.
A search for high-energy neutrino emission correlated with gamma-ray bursts outside the electromagnetic prompt-emission time window is presented. Using a stacking approach of the time delays between reported gamma-ray burst alerts and spatially coincident muon-neutrino signatures, data from the Antares neutrino telescope recorded between 2007 and 2012 are analysed. One year of public data from the IceCube detector between 2008 and 2009 have been also investigated. The respective timing profiles are scanned for statistically significant accumulations within 40 days of the Gamma Ray Burst, as expected from Lorentz Invariance Violation effects and some astrophysical models. No significant excess over the expected accidental coincidence rate could be found in either of the two data sets. The average strength of the neutrino signal is found to be fainter than one detectable neutrino signal per hundred gamma-ray bursts in the Antares data at 90% confidence level.
We develop the formalism of holographic renormalization to compute two-point functions in a holographic Kondo model. The model describes a (0 + 1)-dimensional impurity spin of a gauged SU(N ) interacting with a (1 + 1)-dimensional, large-N , strongly-coupled Conformal Field Theory (CFT). We describe the impurity using Abrikosov pseudo-fermions, and define an SU(N )-invariant scalar operator O built from a pseudo-fermion and a CFT fermion. At large N the Kondo interaction is of the form O\(^{†}\)O, which is marginally relevant, and generates a Renormalization Group (RG) flow at the impurity. A second-order mean-field phase transition occurs in which O condenses below a critical temperature, leading to the Kondo effect, including screening of the impurity. Via holography, the phase transition is dual to holographic superconductivity in (1 + 1)-dimensional Anti-de Sitter space. At all temperatures, spectral functions of O exhibit a Fano resonance, characteristic of a continuum of states interacting with an isolated resonance. In contrast to Fano resonances observed for example in quantum dots, our continuum and resonance arise from a (0 + 1)-dimensional UV fixed point and RG flow, respectively. In the low-temperature phase, the resonance comes from a pole in the Green’s function of the form −i〈O〉\(^{2}\), which is characteristic of a Kondo resonance.
The electrodynamics of topological insulators (TIs) is described by modified Maxwell’s equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of α/4π per surface. Here we report on the observation of this so-called topological magnetoelectric effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semitransparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant α=e\(^{2}\)/2E\(_{0}\)hc (in SI units) when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.
The production of a neutral and a charged vector boson with subsequent decays into three charged leptons and a neutrino is a very important process for precision tests of the Standard Model of elementary particles and in searches for anomalous triple-gauge-boson couplings. In this article, the first computation of next-to-leading-order electroweak corrections to the production of the four-lepton final states μ\(^{+}\)μ\(^{−}\)e\(^{+}\)ν\(_{e}\), μ\(^{+}\)μ\(^{−}\)e\(^{−}\)ν\(_{e}\), μ\(^{+}\)μ\(^{−}\)μ\(^{+}\)ν\(_{μ}\), and μ\(^{+}\)μ\(^{−}\)μ\(^{−}\)ν\(_{μ}\) at the Large Hadron Collider is presented. We use the complete matrix elements at leading and next-to-leading order, including all off-shell effects of intermediate massive vector bosons and virtual photons. The relative electroweak corrections to the fiducial cross sections from quark-induced partonic processes vary between −3% and −6%, depending significantly on the event selection. At the level of differential distributions, we observe large negative corrections of up to −30% in the high-energy tails of distributions originating from electroweak Sudakov logarithms. Photon-induced contributions at next-to-leading order raise the leading-order fiducial cross section by +2%. Interference effects in final states with equal-flavour leptons are at the permille level for the fiducial cross section, but can lead to sizeable effects in off-shell sensitive phase-space regions.
Paramagnetic heavy fermion insulators consist of fully occupied quasiparticle bands inherent to Fermi liquid theory. The gap emergence below a characteristic temperature is the ultimate sign of coherence for a many-body system, which in addition can induce a non-trivial band topology. Here, we demonstrate a simple and efficient method to compare a model study and an experimental result for heavy fermion insulators. The temperature dependence of the gap formation in both local moment and mixed valence regimes is captured within the dynamical mean field (DMFT) approximation to the periodic Anderson model (PAM). Using the topological coherence temperature as the scaling factor and choosing the input parameter set within the mixed valence regime, we can unambiguously link the theoretical energy scales to the experimental ones. As a particularly important result, we find improved consistency between the scaled DMFT density of states and the photoemission near-gap spectra of samarium hexaboride (SmB\(_{6}\)).
We present the computer code RECOLA2 along with the first NLO electroweak corrections to Higgs production in vector-boson fusion and updated results for Higgs strahlung in the Two-Higgs-Doublet Model and Higgs-Singlet extension of the Standard Model. A fully automated procedure for the generation of tree-level and one-loop matrix elements in general models, including renormalization, is presented. We discuss the application of the Background-Field Method to the extended models. Numerical results for NLO electroweak cross sections are presented for different renormalization schemes in the Two-Higgs-Doublet Model and the Higgs-Singlet extension of the Standard Model. Finally, we present distributions for the production of a heavy Higgs boson.
We analyze the concomitant spontaneous breaking of translation and conformal symmetries by introducing in a CFT a complex scalar operator that acquires a spatially dependent expectation value. The model, inspired by the holographic Q-lattice, provides a privileged setup to study the emergence of phonons from a spontaneous translational symmetry breaking in a conformal field theory and offers valuable hints for the treatment of phonons in QFT at large. We first analyze the Ward identity structure by means of standard QFT techniques, considering both spontaneous and explicit symmetry breaking. Next, by implementing holographic renormalization, we show that the same set of Ward identities holds in the holographic Q-lattice. Eventually, relying on the holographic and QFT results, we study the correlators realizing the symmetry breaking pattern and how they encode information about the low-energy spectrum.
Complete NLO corrections to W\(^{+}\)W\(^{+}\) scattering and its irreducible background at the LHC
(2017)
The process pp → μ\(^{+}\)ν\(_{μ}\)e\(^{+}\)ν\(_{e}\)jj receives several contributions of different orders in the strong and electroweak coupling constants. Using appropriate event selections, this process is dominated by vector-boson scattering (VBS) and has recently been measured at the LHC. It is thus of prime importance to estimate precisely each contribution. In this article we compute for the first time the full NLO QCD and electroweak corrections to VBS and its irreducible background processes with realistic experimental cuts. We do not rely on approximations but use complete amplitudes involving two different orders at tree level and three different orders at one-loop level. Since we take into account all interferences, at NLO level the corrections to the VBS process and to the QCD-induced irreducible background process contribute at the same orders. Hence the two processes cannot be unambiguously distinguished, and all contributions to the μ\(^{+}\)ν\(_{μ}\)e\(^{+}\)ν\(_{e}\)jj final state should be preferably measured together.
Some Bravais lattices have a particular geometry that can slow down the motion of Bloch electrons by pre-localization due to the band-structure properties. Another known source of electronic localization in solids is the Coulomb repulsion in partially filled d or f orbitals, which leads to the formation of local magnetic moments. The combination of these two effects is usually considered of little relevance to strongly correlated materials. Here we show that it represents, instead, the underlying physical mechanism in two of the most important ferromagnets: nickel and iron. In nickel, the van Hove singularity has an unexpected impact on the magnetism. As a result, the electron–electron scattering rate is linear in temperature, in violation of the conventional Landau theory of metals. This is true even at Earth’s core pressures, at which iron is instead a good Fermi liquid. The importance of nickel in models of geomagnetism may have therefore to be reconsidered.
Flux distribution is an important tool to understand the variability processes in activegalactic nuclei. We now have available a great deal of observational evidences pointing towards thepresence of log-normal components in the high energy light curves, and different models have beenproposed to explain these data. Here, we collect some of the recent developments on this topic usingthe well-known blazar Mrk 501 as example of complex and interesting aspects coming from its fluxdistribution in different energy ranges and at different timescales. The observational data we refer toare those collected in a complementary manner by Fermi-LAT over multiple years, and by the FirstG-APD Cherenkov Telescope (FACT) telescope and the H.E.S.S. array in correspondence of the brightflare of June 2014
The electric and nonvolatile control of the spin texture in semiconductors would represent a fundamental step toward novel electronic devices combining memory and computing functionalities. Recently, GeTe has been theoretically proposed as the father compound of a new class of materials, namely ferroelectric Rashba semiconductors. They display bulk bands with giant Rashba-like splitting due to the inversion symmetry breaking arising from the ferroelectric polarization, thus allowing for the ferroelectric control of the spin. Here, we provide the experimental demonstration of the correlation between ferroelectricity and spin texture. A surface-engineering strategy is used to set two opposite predefined uniform ferroelectric polarizations, inward and outward, as monitored by piezoresponse force microscopy. Spin and angular resolved photoemission experiments show that these GeTe(111) surfaces display opposite sense of circulation of spin in bulk Rashba bands. Furthermore, we demonstrate the crafting of nonvolatile ferroelectric patterns in GeTe films at the nanoscale by using the conductive tip of an atomic force microscope. Based on the intimate link between ferroelectric polarization and spin in GeTe, ferroelectric patterning paves the way to the investigation of devices with engineered spin configurations.
This Thesis investigates the interplay of a central degree of freedom with an environment. Thereby, the environment is prepared in a localized phase of matter.
The long-term aim of this setup is to store quantum information on the central degree of freedom while exploiting the advantages of localized systems.
These many-body localized systems fail to equilibrate under the description of thermodynamics, mostly due to disorder. Doing so, they form the most prominent phase of matter that violates the eigenstate thermalization hypothesis. Thus, many-body localized systems preserve information about an initial state until infinite times without the necessity to isolate the system.
This unique feature clearly suggests to store quantum information within localized environments, whenever isolation is impracticable.
After an introduction to the relevant concepts, this Thesis examines to which extent a localized phase of matter may exist at all if a central degree of freedom dismantles the notion of locality in the first place. To this end, a central spin is coupled to the disordered Heisenberg spin chain, which shows many-body localization. Furthermore, a noninteracting analog describing free fermions is discussed. Therein, an impurity is coupled to an Anderson localized environment.
It is found that in both cases, the presence of the central degree of freedom manifests in many properties of the localized environment. However, for a sufficiently weak coupling, quantum chaos, and thus, thermalization is absent. In fact, it is shown that the critical disorder, at which the metal-insulator transition of its environment occurs in the absence of the central degree of freedom, is modified by the coupling strength of the central degree of freedom. To demonstrate this, a phase diagram is derived.
Within the localized phase, logarithmic growth of entanglement entropy, a typical signature of many-body localized systems, is increased by the coupling to the central spin. This property is traced back to resonantly coupling spins within the localized Heisenberg chain and analytically derived in the absence of interactions. Thus, the studied model of free fermions is the first model without interactions that mimics the logarithmic spreading of entanglement entropy known from many-body localized systems.
Eventually, it is demonstrated that observables regarding the central spin significantly break the eigenstate thermalization hypothesis within the localized phase. Therefore, it is demonstrated how a central spin can be employed as a detector of many-body localization.
Long-term monitoring of the ANTARES optical module efficiencies using \(^{40}\)K decays in sea water
(2018)
Cherenkov light induced by radioactive decay products is one of the major sources of background light for deep-sea neutrino telescopes such as ANTARES. These decays are at the same time a powerful calibration source. Using data collected by the ANTARES neutrino telescope from mid 2008 to 2017, the time evolution of the photon detection efficiency of optical modules is studied. A modest loss of only 20% in 9 years is observed. The relative time calibration between adjacent modules is derived as well.
The modular Hamiltonian of reduced states, given essentially by the logarithm of the reduced density matrix, plays an important role within the AdS/CFT correspondence in view of its relation to quantum information. In particular, it is an essential ingredient for quantum information measures of distances between states, such as the relative entropy and the Fisher information metric. However, the modular Hamiltonian is known explicitly only for a few examples. For a family of states rho(lambda) that is parametrized by a scalar lambda, the first order contribution in (lambda) over tilde = lambda-lambda(0) of the modular Hamiltonian to the relative entropy between rho(lambda) and a reference state rho(lambda 0) is completely determined by the entanglement entropy, via the first law of entanglement. For several examples, e.g. for ball-shaped regions in the ground state of CFTs, higher order contributions are known to vanish. In these cases the modular Hamiltonian contributes to the Fisher information metric in a trivial way. We investigate under which conditions the modular Hamiltonian provides a non-trivial contribution to the Fisher information metric, i.e. when the contribution of the modular Hamiltonian to the relative entropy is of higher order in (lambda) over tilde. We consider one-parameter families of reduced states on two entangling regions that form an entanglement plateau, i.e. the entanglement entropies of the two regions saturate the Araki-Lieb inequality. We show that in general, at least one of the relative entropies of the two entangling regions is expected to involve (lambda) over tilde contributions of higher order from the modular Hamiltonian. Furthermore, we consider the implications of this observation for prominent AdS/CFT examples that form entanglement plateaux in the large N limit.
Sufficiently disordered metals display systematic deviations from the behavior predicted by semi-classical Boltzmann transport theory. Here the scattering events from impurities or thermal excitations can no longer be considered as additive-independent processes, as asserted by Matthiessen’s rule following from this picture. In the intermediate region between the regime of good conduction and that of insulation, one typically finds a change of sign of the temperature coefficient of resistivity, even at elevated temperature spanning ambient conditions, a phenomenology that was first identified by Mooij in 1973. Traditional weak coupling approaches to identify relevant corrections to the Boltzmann picture focused on long-distance interference effects such as “weak localization”, which are especially important in low dimensions (1D and 2D) and close to the zero-temperature limit. Here we formulate a strong-coupling approach to tackle the interplay of strong disorder and lattice deformations (phonons) in bulk three-dimensional metals at high temperatures. We identify a polaronic mechanism of strong disorder renormalization, which describes how a lattice locally responds to the relevant impurity potential. This mechanism, which quantitatively captures the Mooij regime, is physically distinct and unrelated to Anderson localization, but realizes early seminal ideas of Anderson himself, concerning the interplay of disorder and lattice deformations.
Active galactic nuclei (AGN) are among the brightest and most frequent sources on the extragalactic X-ray and gamma-ray sky. Their central supermassive blackhole generates an enormous luminostiy through accretion of the surrounding gas. A few AGN harbor highly collimated, powerful jets in which are observed across the entire electromagnetic spectrum. If their jet axis is seen in a small angle to our line-of-sight (these objects are then called blazars) jet emission can outshine any other emission component from the system. Synchrotron emission from electrons and positrons clearly prove the existence of a relativistic leptonic component in the jet plasma. But until today, it is still an open question whether heavier particles, especially protons, are accelerated as well. If this is the case, AGN would be prime candidates for extragalactic PeV neutrino sources that are observed on Earth. Characteristic signatures for protons can be hidden in the variable high-energy emission of these objects. In this thesis I investigated the broadband emission, particularly the high-energy X-ray and gamma-ray emission of jetted AGN to address open questions regarding the particle acceleration and particle content of AGN jets, or the evolutionary state of the AGN itself. For this purpose I analyzed various multiwavelength observations from optical to gamma-rays over a period of time using a combination of state-of-the-art spectroscopy and timing analysis. By nature, AGN are highly variable. Time-resolved spectral analysis provided a new dynamic view of these sources which helped to determine distinct emission processes that are difficult to disentangle from spectral or timing methods alone.
Firstly, this thesis tackles the problem of source classification in order to facilitate the search for interesting sources in large data archives and characterize new transient sources. I use spectral and timing analysis methods and supervised machine learning algorithms to design an automated source classification pipeline. The test and training sample were based on the third XMM-Newton point source catalog (3XMM-DR6). The set of input features for the machine learning algorithm was derived from an automated spectral modeling of all sources in the 3XMM-DR6, summing up to 137200 individual detections. The spectral features were complemented by results of a basic timing analysis as well as multiwavelength information provided by catalog cross-matches. The training of the algorithm and application to a test sample showed that the definition of the training sample was crucial: Despite oversampling minority source types with synthetic data to balance out the training sample, the algorithm preferably predicted majority source types for unclassified objects. In general, the training process showed that the combination of spectral, timing and multiwavelength features performed best with the lowest misclassification rate of \\sim2.4\\%.
The methods of time-resolved spectroscopy was then used in two studies to investigate the properties of two individual AGN, Mrk 421 and PKS 2004-447, in detail. Both objects belong to the class of gamma-ray emitting AGN. A very elusive sub-class are gamma-ray emitting Narrow Line Seyfert 1 (gNLS1) galaxies. These sources have been discovered as gamma-ray sources only recently in 2010 and a connection to young radio galaxies especially compact steep spectrum (CSS) radio sources has been proposed. The only gNLS1 on the Southern Hemisphere so far is PKS2004-447 which lies at the lower end of the luminosity distribution of gNLS1. The source is part of the TANAMI VLBI program and is regularly monitored at radio frequencies. In this thesis, I presented and analyzed data from a dedicated multiwavelength campaign of PKS 2004-447 which I and my collaborators performed during 2012 and which was complemented by individual observations between 2013 and 2016. I focussed on the detailed analysis of the X-ray emission and a first analysis of its broadband spectrum from radio to gamma-rays. Thanks to the dynamic SED I could show that earlier studies misinterpreted the optical spectrum of the source which had led to an underestimation of the high-energy emission and had ignited a discussion on the source class. I show that the overall spectral properties are consistent with dominating jet emission comprised of synchrotron radiation and inverse Compton scattering from accelerated leptons. The broadband emission is very similar to typical examples of a certain type of blazars (flat-spectrum radio quasars) and does not present any unusual properties in comparison. Interestingly, the VLBI data showed a compact jet structure and a steep radio spectrum consistent with a compact steep spectrum source. This classified PKS 2004-447 as a young radio galaxy, in which the jet is still developing.
The investigation of Mrk 421 introduced the blazar monitoring program which I and collaborator have started in 2014. By observing a blazar simultaneously from optical, X-ray and gamma-ray bands during a VHE outbursts, the program aims at providing extraordinary data sets to allow for the generation of a series of dynamical SEDs of high spectral and temporal resolution. The program makes use of the dense VHE monitoring by the FACT telescope. So far, there are three sources in our sample that we have been monitoring since 2014. I presented the data and the first analysis of one of the brightest and most variable blazar, Mrk 421, which had a moderate outbreak in 2015 and triggered our program for the first time. With spectral timing analysis, I confirmed a tight correlation between the X-ray and TeV energy bands, which indicated that these jet emission components are causally connected. I discovered that the variations of the optical band were both correlated and anti-correlated with the high-energy emission, which suggested an independent emission component. Furthermore, the dynamic SEDs showed two different flaring behaviors, which differed in the presence or lack of a peak shift of the low-energy emission hump. These results further supported the hypothesis that more than one emission region contributed to the broadband emission of Mrk 421 during the observations.
Overall,the studies presented in this thesis demonstrated that time-resolved spectroscopy is a powerful tool to classify both source types and emission processes of astronomical objects, especially relativistic jets in AGN, and thus provide a deeper understanding and new insights of their physics and properties.
This dissertation employs gauge/gravity duality to investigate features
of ( 2 + 1 ) -dimensional quantum gravity in Anti-de Sitter space (AdS)
and its relation to conformal field theory (CFT) in 1 + 1 dimensions.
Concretely, we contribute to research on the frontier of gauge/gravity
with condensed matter as well as the frontier with quantum informa-
tion.
The first research topic of this thesis is motivated by the Kondo
model, which describes the screening of magnetic impurities in metals
by conduction electrons at low temperatures. This process has a de-
scription in the language of string theory via fluctuating surfaces in
spacetime, called branes. At high temperatures the unscreened Kondo
impurity is modelled by a stack of pointlike branes. At low tempera-
tures this stack condenses into a single spherical, two-dimensional brane
which embodies the screened impurity.
This thesis demonstrates how this condensation process is naturally
reinvoked in the holographic D1/D5 system. We find brane configu-
rations mimicking the Kondo impurities at high and low energies and
establish the corresponding brane condensation, where the brane grows
two additional dimensions. We construct supergravity solutions, which
fully take into account the effect of the brane on its surrounding space-
time before and after the condensation takes place. This enables us
to compute the full impurity entropies through which we confirm the
validity of the g-theorem.
The second research topic is rooted in the connection of geometry
with quantum information. The motivation stems from the “complexity
equals volume” proposal, which relates the volume of wormholes to
the cicruit complexity of a thermal quantum state. We approach this
proposal from a pragmatic point of view by studying the properties of
certain volumes in gravity and their description in the CFT.
We study subregion complexities, which are the volumes of the re-
gions subtended by Ryu-Takayanagi (RT) geodesics. On the gravity
side we reveal their topological properties in the vacuum and in ther-
mal states, where they turn out to be temperature independent. On the
field theory side we develop and proof a formula using kinematic space
which computes subregion complexities without referencing the bulk.
We apply our formula to global AdS 3 , the conical defect and a black
hole. While entanglement, i.e. minimal boundary anchored geodesics,
suffices to produce vacuum geometries, for the conical defect we also
need geodesics windings non-trivially around the singularity. The black
hole geometry requires additional thermal contributions.
Active Galactic Nuclei (AGNs) are among the most powerful and most intensively studied objects in the Universe. AGNs harbor a mass accreting supermassive black hole (SMBH) in their center and emit radiation throughout the entire electromagnetic spectrum. About 10% show relativistic particle outflows, perpendicular to the so-called accretion disk, which are known as jets. Blazars, a subclass of AGN with jet orientations close to the line-of-sight of the observer, are highly variable sources from radio to TeV energies and dominate the γ- ray sky. The overall observed broadband emission of blazars is characterized by two distinct emission humps. While the low-energy hump is well described by synchrotron radiation of relativistic electrons, both leptonic processes such as inverse Compton scattering and hadronic processes such as pion-photoproduction can explain the radiation measured in the high-energy hump. Neutrinos, neutral, nearly massless particles, which only couple to the weak force 1 are exclusively produced in hadronic interactions of protons accelerated to relativistic energies. The detection of a high-energy neutrino from an AGN would provide an irrefutable proof of hadronic processes happening in jets. Recently, the IceCube neutrino observatory, located at the South Pole with a total instrumented volume of about one km 3 , provided evidence for a diffuse high-energy neutrino flux. Since the atmospheric neutrino spectrum falls steeply with energy, individual events with the clearest signature of coming from an extraterrestrial origin are those at the highest energies. These events are uniformly distributed over the entire sky and are therefore most likely of extragalactic nature. While the neutrino event (known as “BigBird”) with a reconstructed energy of ∼ 2 PeV has already been detected in temporal and spatial agreement with a single blazar in an active phase, still, the chance coincidence for such an association is only on the order of ∼ 5%. The neutrino flux at these high energies is low, so that even the brightest blazars only yield a Poisson probability clearly below unity. Such a small probability is in agreement with the observed all-sky neutrino flux otherwise, the sky would already be populated with numerous confirmed neutrino point sources. In neutrino detectors, events are typically detected in two different signatures 2 . So-called shower-like electron neutrino events produce a large particle cascade, which leads to a pre- cise energy measurement, but causes a large angular uncertainty. Track-like muon neutrino events, however, only produce a single trace in the detector, leading to a precise localization but poor energy reconstruction. The “BigBird” event was a shower-like neutrino event, tem- porally coincident with an activity phase of the blazar PKS 1424−418, lasting several months. Shower-like neutrino events typically lead to an angular resolution of ∼ 10 ◦ , while track-like events show a localization uncertainty of only ∼ 1 ◦ . Considering the potential detection of a track-like neutrino event in agreement with an activity phase of a single blazar lasting only days would significantly decrease the chance coincidence of such an association. In this thesis, a sample of bright blazars, continuously monitored by Fermi/LAT in the MeV to GeV regime, is considered as potential neutrino candidates. I studied the maximum possible neutrino ex- pectation of short-term blazar flares with durations of days to weeks, based on a calorimetric argumentation. I found that the calorimetric neutrino output of most short-term blazar flares is too small to lead to a substantial neutrino detection. However, for the most extreme flares, Poisson probabilities of up to ∼ 2% are reached, so that the possibility of associated neutrino detections in future data unblindings of IceCube and KM3NeT seems reasonable. On 22 September 2017, IceCube detected the first track-like neutrino event (named IceCube- 170922A) coincident with a single blazar in an active phase. From that time on, the BL Lac object TXS 0506+056 was subject of an enormous multiwavelength campaign, revealing an en- hanced flux state at the time of the neutrino arrival throughout several different wavelengths. In this thesis, I first studied the long-term flaring behavior of TXS 0506+056, using more than nine years of Fermi/LAT data. I found that the activity phase in the MeV to GeV regime already started in early 2017, months before the arrival of IceCube-170922A. I performed a calorimetric analysis on a 3-day period around the neutrino arrival time and found no sub- stantial neutrino expectation from such a short time range. By computing the calorimetric neutrino prediction for the entire activity phase of TXS 0506+056 since early 2017, a possible association seems much more likely. However, the post-trial corrected chance coincidence for a long-term association between IceCube-170922A and the blazar TXS 0506+056 is on the level of ∼ 3.5 σ, establishing TXS 0506+056 as the most promising neutrino point source candidate in the scientific community. Another way to explain a high-energy neutrino signal without an observed astronomical counterpart, would be the consideration of blazars at large cosmological distances. These high-redshift blazars are capable of generating the observed high-energy neutrino flux, while their γ-ray emission would be efficiently downscattered by Extragalactic Background Light (EBL), making them almost undetectable to Fermi/LAT. High-redshift blazars are impor- tant targets, as they serve as cosmological probes and represent one of the most powerful classes of γ-ray sources in the Universe. Unfortunately, only a small number of such objects could be detected with Fermi/LAT so far. In this thesis, I perform a systematic search for flaring events in high-redshift γ-ray blazars, which long-term flux is just below the sensitiv- ity limit of Fermi/LAT. By considering a sample of 176 radio detected high-redshift blazars, undetected at γ-ray energies, I was able to increase the number of previously unknown γ-ray blazars by a total of seven sources. Especially the blazar 5BZQ J2219−2719, at a distance of z = 3.63 was found to be the most distant new γ-ray source identified within this thesis. In the final part of this thesis, I studied the flaring behavior of bright blazars, previously considered as potential neutrino candidates. While the occurrence of flaring intervals in blazars is of purely statistical nature, I found potential differences in the observed flaring behavior of different blazar types. Blazars can be subdivided into BL Lac (BLL) objects, Flat-Spectrum Radio Quasar (FSRQ) and Blazars Candidates of Uncertain type (BCU). FSRQs are typ- ically brighter than BL Lac or BCU type blazars, thus longer flares and more complicated substructures can be resolved. Although BL Lacs and BCUs are capable of generating signifi- cant flaring episodes, they are often identified close to the detection threshold of Fermi/LAT. Long-term outburst periods are exclusively observed in FSRQs, while BCUs can still con- tribute with flare durations of up to ten days. BL Lacs, however, are only detected in flaring states of less than four days. FSRQs are bright enough to be detected multiple times with time gaps between two subsequent flaring intervals ranging between days and months. While BL Lacs can show time gaps of more than 100 days, BCUs are only observed with gaps up to 20 days, indicating that these objects are detected only once in the considered time range of six years. The newly introduced parameter “Boxyness” describes the averaged flux in an identified flaring state and does highly depend on the shape of the considered flare. While perfectly box-like flares (flares which show a constant flux level over the entire time range) correspond to an averaged flux which is equal the maximum flare amplitude, irregular shaped flares generate a smaller averaged flux. While all blazar types show perfectly box-shaped daily flares, BL Lacs and BCUs are typically not bright enough to be resolved for multiple days. The work presented in this thesis illustrates the challenging state of multimessenger neu- trino astronomy and the demanding hunt for the first extragalactic neutrino point sources. In this context, this work discusses the multiwavelength emission behavior of blazars as a promising class of neutrino point sources and allows for predictions of current and future source associations
In the past few years, two-dimensional quantum liquids with fractional excitations have been a topic of high interest due to their possible application in the emerging field of quantum computation and cryptography. This thesis is devoted to a deeper understanding of known and new fractional quantum Hall states and their stabilization in local models. We pursue two different paths, namely chiral spin liquids and fractionally quantized, topological phases.
The chiral spin liquid is one of the few examples of spin liquids with fractional statistics. Despite its numerous promising properties, the microscopic models for this state proposed so far are all based on non-local interactions, making the experimental realization challenging. In the first part of this thesis, we present the first local parent Hamiltonians, for which the Abelian and non-Abelian chiral spin liquids are the exact and, modulo a topological degeneracy, unique ground states. We have developed a systematic approach to find an annihilation operator of the chiral spin liquid and construct from it a many-body interaction which establishes locality. For various system sizes and lattice geometries, we numerically find largely gapped eigenspectra and confirm to an accuracy of machine precision the uniqueness of the chiral spin liquid as ground state of the respective system. Our results provide an exact spin model in which fractional quantization can be studied.
Topological insulators are one of the most actively studied topics in current condensed matter physics research. With the discovery of the topological insulator, one question emerged: Is there an interaction-driven set of fractionalized phases with time reversal symmetry? One intuitive approach to the theoretical construction of such a fractional topological insulator is to take the direct product of a fractional quantum Hall state and its time reversal conjugate. However, such states are well studied conceptually and do not lead to new physics, as the idea of taking a state and its mirror image together without any entanglement between the states has been well understood in the context of topological insulators. Therefore, the community has been looking for ways to implement some topological interlocking between different spin species. Yet, for all practical purposes so far, time reversal symmetry has appeared to limit the set of possible fractional states to those with no interlocking between the two spin species.
In the second part of this thesis, we propose a new universality class of fractionally quantized, topologically ordered insulators, which we name “fractional insulator”. Inspired by the fractional quantum Hall effect, spin liquids, and fractional Chern insulators, we develop a wave function approach to a new class of topological order in a two-dimensional crystal of spin-orbit coupled electrons. The idea is simply to allow the topological order to violate time reversal symmetry, while all locally observable quantities remain time reversal invariant. We refer to this situation as “topological time reversal symmetry breaking”. Our state is based on the Halperin double layer states and can be viewed as a two-layer system of an ↑-spin and a ↓-spin sphere. The construction starts off with Laughlin states for the ↑-spin and ↓-spin electrons and an interflavor term, which creates correlations between the two layers. With a careful parameter choice, we obtain a state preserving time reversal symmetry locally, and label it the “311-state”. For systems of up to six ↑-spin and six ↓-spin electrons, we manage to construct an approximate parent Hamiltonian with a physically realistic, local interaction.
The helical distribution of the electronic density in chiral molecules, such as DNA and bacteriorhodopsin, has been suggested to induce a spin–orbit coupling interaction that may lead to the so-called chirality-induced spin selectivity (CISS) effect. Key ingredients for the theoretical modelling are, in this context, the helically shaped potential of the molecule and, concomitantly, a Rashba-like spin–orbit coupling due to the appearance of a magnetic field in the electron reference frame. Symmetries of these models clearly play a crucial role in explaining the observed effect, but a thorough analysis has been largely ignored in the literature. In this work, we present a study of these symmetries and how they can be exploited to enhance chiral-induced spin selectivity in helical molecular systems.
Active Galactic Nuclei emit radiation over the whole electromagnetic spectrum up to TeV energies. Blazars are one subtype with their jets pointing towards the observer. One of their typical features is extreme variability on timescales, from minutes to years. The fractional variability is an often used parameter for investigating the degree of variability of a light curve. Different detection methods and sensitivities of the instruments result in differently binned data and light curves with gaps. As they can influence the physics interpretation of the broadband variability, the effects of these differences on the fractional variability need to be studied. In this paper, we study the systematic effects of completeness in time coverage and the sampling rate. Using public data from instruments monitoring blazars in various energy ranges, we study the variability of the bright TeV blazars Mrk 421 and Mrk 501 over the electromagnetic spectrum, taking into account the systematic effects, and compare our findings with previous results. Especially in the TeV range, the fractional variability is higher than in previous studies, which can be explained by the much longer (seven years compared to few weeks) and more complete data sample.
For the understanding of the variable, transient and non-thermal universe, unbiased long-term monitoring is crucial. To constrain the emission mechanisms at the highest energies, it is important to characterize the very high energy emission and its correlation with observations at other wavelengths. At very high energies, only a limited number of instruments is available. This article reviews the current status of monitoring of the extra-galactic sky at TeV energies.
The topic of this thesis is generalizations of the Anti de Sitter/Conformal Field Theory (AdS/CFT) correspondence, often referred to as holography, and their application to models relevant for condensed matter physics. A particular virtue of AdS/CFT is to map strongly coupled quantum field theories, for which calculations are inherently difficult, to more tractable classical gravity theories. I use this approach to study the crossover between Bose-Einstein condensation (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superconductivity mechanism. I also study the phase transitions between the AdS black hole and AdS soliton spacetime in the presence of disorder. Moreover, I consider a holographic model of a spin impurity interacting with a strongly correlated electron gas, similar to the Kondo model.
In AdS/CFT, the BEC/BCS crossover is modeled by a soliton configuration in the dual geometry and we study the BEC and BCS limits. The backreaction of the matter field on the background geometry is considered, which provides a new approach to study the BEC/BCS crossover. The behaviors of some physical quantities such as depletion of charge density under different strength of backreaction are presented and discussed. Moreover, the backreaction enables us to obtain the effective energy density of the soliton configurations, which together with the surface tension of the solitons leads to an argument for the occurrence of so called snake instability for dark solitons, i.e. for the solitons to form a vortex-like structures.
Disordering strongly coupled and correlated quantum states of matter may lead to new insights into the physics of many body localized (MBL) strongly correlated states, which may occur in the presence of strong disorder. We are interested in potential insulator-metal transitions induced by disorder, and how disorder affects the Hawking-Page phase transition in AdS gravity in general. We introduce a metric ansatz and numerically construct the corresponding disordered AdS soliton and AdS black hole solutions, and discuss the calculation of the free energy in these states.
In the Kondo effect, the rise in resistivity in metals with scarce magnetic impurities at low temperatures can be explained by the RG flow of the antiferromagnetic coupling between the impurity and conduction electrons in CFT. The generalizations to SU(N) in the large N limit make the treatment amenable to the holographic approach. We add a Maxwell term to a previously existing holographic model to study the conductivity of the itinerant electrons. Our goal is to find the log(T) behavior in the DC resistivity. In the probe limit, we introduce junction conditions to connect fields crossing the defect. We then consider backreactions, which give us a new metric ansatz and new junction conditions for the gauge fields.
In recent years many discoveries have been made that reveal a close relation between quantum information and geometry in the context of the AdS/CFT correspondence. In this duality between a conformal quantum field theory (CFT) and a theory of gravity on Anti-de Sitter spaces (AdS) quantum information quantities in CFT are associated with geometric objects in AdS. Subject of this thesis is the examination of this intriguing property of AdS/CFT. We study two central elements of quantum information: subregion complexity -- which is a measure for the effort required to construct a given reduced state -- and the modular Hamiltonian -- which is given by the logarithm of a considered reduced state.
While a clear definition for subregion complexity in terms of unitary gates exists for discrete systems, a rigorous formulation for quantum field theories is not known.
In AdS/CFT, subregion complexity is proposed to be related to certain codimension one regions on the AdS side.
The main focus of this thesis lies on the examination of such candidates for gravitational duals of subregion complexity.
We introduce the concept of \textit{topological complexity}, which considers subregion complexity to be given by the integral over the Ricci scalar of codimension one regions in AdS. The Gauss-Bonnet theorem provides very general expressions for the topological complexity of CFT\(_2\) states dual to global AdS\(_3\), BTZ black holes and conical defects. In particular, our calculations show that the topology of the considered codimension one bulk region plays an essential role for topological complexity.
Moreover, we study holographic subregion complexity (HSRC), which associates the volume of a particular codimension one bulk region with subregion complexity. We derive an explicit field theory expression for the HSRC of vacuum states. The formulation of HSRC in terms of field theory quantities may allow to investigate whether this bulk object indeed provides a concept of subregion complexity on the CFT side. In particular, if this turns out to be the case, our expression for HSRC may be seen as a field theory definition of subregion complexity. We extend our expression to states dual to BTZ black holes and conical defects.
A further focus of this thesis is the modular Hamiltonian of a family of states \(\rho_\lambda\) depending on a continuous parameter \(\lambda\). Here \(\lambda\) may be associated with the energy density or the temperature, for instance.
The importance of the modular Hamiltonian for quantum information is due to its contribution to relative entropy -- one of the very few objects in quantum information with a rigorous definition for quantum field theories.
The first order contribution in \(\tilde{\lambda}=\lambda-\lambda_0\) of the modular Hamiltonian to the relative entropy between \(\rho_\lambda\) and a reference state \(\rho_{\lambda_0}\) is provided by the first law of entanglement. We study under which circumstances higher order contributions in \(\tilde{\lambda}\) are to be expected.
We show that for states reduced to two entangling regions \(A\), \(B\) the modular Hamiltonian of at least one of these regions is expected to provide higher order contributions in \(\tilde{\lambda}\) to the relative entropy if \(A\) and \(B\) saturate the Araki-Lieb inequality. The statement of the Araki-Lieb inequality is that the difference between the entanglement entropies of \(A\) and \(B\) is always smaller or equal to the entanglement entropy of the union of \(A\) and \(B\).
Regions for which this inequality is saturated are referred to as entanglement plateaux. In AdS/CFT the relation between geometry and quantum information provides many examples for entanglement plateaux. We apply our result to several of them, including large intervals for states dual to BTZ black holes and annuli for states dual to black brane geometries.
The quest for finding a unifying theory for both quantum theory and gravity lies at the heart of much of the research in high energy physics. Although recent years have witnessed spectacular experimental confirmation of our expectations from Quantum Field Theory and General Relativity, the question of unification remains as a major open problem. In this context, the perturbative aspects of quantum black holes represent arguably the best of our knowledge of how to proceed in this pursue.
In this thesis we investigate certain aspects of quantum gravity in 2 + 1 dimensional anti-de Sitter space (AdS3), and its connection to Conformal field theories in 1 + 1 dimensions (CFT2), via the AdS/CFT correspondence.
We study the thermodynamics properties of higher spin black holes. By focusing on the spin-4 case, we show that black holes carrying higher spin charges display a rich phase diagram in the grand canonical ensemble, including phase transitions of the Hawking-Page type, first order inter-black hole transitions, and a second order critical point.
We investigate recent proposals on the connection between bulk codimension-1 volumes and computational complexity in the CFT. Using Tensor Networks we provide concrete evidence of why these bulk volumes are related to the number of gates in a quantum circuit, and exhibit their topological properties. We provide a novel formula to compute this complexity directly in terms of entanglement entropies, using techniques from Kinematic space.
We then move in a slightly different direction, and study the quantum properties of black holes via de Functional Renormalisation Group prescription coming from Asymptotic safety. We avoid the arbitrary scale setting by restricting to a narrower window in parameter space, where only Newton’s coupling and the cosmological constant are allowed to vary. By one assumption on the properties of Newton’s coupling, we find black hole solutions explicitly. We explore their thermodynamical properties, and discover that very large black holes exhibit very unusual features.
Despite its history of more than one hundred years, the phenomenon of
superconductivity has not lost any of its allure. During that time the concept
and perception of the superconducting state - both from an experimental and
theoretical point of view - has evolved in way that has
triggered increasing interest. What was initially believed to simply be the
disappearance of electrical resistivity, turned out to be a universal and
inevitable result of quantum statistics, characterized by many more
aspects apart from its zero resistivity. The insights of
BCS-theory eventually helped to uncover its deep connection to particle physics
and consequently led to the formulation of the Anderson-Higgs-mechanism. The
very core of this theory is the concept of gauge symmetry (breaking). Within the
framework of condensed-matter theory, gauge invariance is only one of several
symmetry groups which are crucial for the description and classification of
superconducting states. \\
In this thesis, we employ time-reversal, inversion, point group and spin
symmetries to investigate and derive possible Hamiltonians featuring spin-orbit
interaction in two and three spatial dimensions.
In particular, this thesis aims at a generalization of existing numerical
concepts to open up the path to spin-orbit coupled (non)centrosymmetric
superconductors in multi-orbital models.
This is done in a two-fold way: On the one hand, we formulate - based on the
Kohn-Luttinger effect - the perturbative renormalization group in the
weak-coupling limit. On the other hand, we define the spinful flow equations of
the effective action in the framework of functional renormalization, which is
valid for finite interaction strength as well. Both perturbative and functional
renormalization groups produce a low-energy effective (spinful) theory that
eventually gives rise to a particular superconducting state, which is investigated
on the level of the irreducible two-particle vertex. The symbiotic relationship
between both perturbative and functional renormalization can be traced back to
the fact that, while the perturbative renormalization at infinitesimal coupling
is only capable of dealing with the Cooper instability, the functional
renormalization can investigate a plethora of instabilities both in the
particle-particle and particle-hole channels. \\
Time-reversal and inversion are the two key symmetries, which are being used to
discriminate between two scenarios. If both time-reversal and inversion symmetry
are present, the Fermi surface will be two-fold degenerate and characterized by a
pseudospin degree of freedom. In contrast, if inversion symmetry is broken, the
Fermi surface will be spin-split and labeled by helicity. In both cases, we
construct the symmetry allowed states in the particle-particle as well as the
particle-hole channel. The methods presented are formally unified and implemented
in a modern object-oriented reusable and extendable C++ code.
This methodological implementation is employed to one member of both families of
pseudospin and helicity characterized systems. For the pseudospin case, we choose
the intriguing matter of strontium ruthenate, which has been heavily
investigated for already twenty-four years, but still keeps puzzling researchers.
Finally, as the helicity based application, we consider the oxide heterostructure
LaAlO$_{3}$/SrTiO$_{3}$, which became famous for its highly mobile two-
dimensional electron gas and is suspected to host topological superconductivity.
One of the main objectives of the ANTARES telescope is the search for point- like neutrino sources. Both the pointing accuracy and the angular resolution of the detector are important in this context and a reliableway to evaluate this performance is needed. In order to measure the pointing accuracy of the detector, one possibility is to study the shadow of the Moon, i. e. the deficit of the atmospheric muon flux from the direction of the Moon induced by the absorption of cosmic rays. Analysing the data taken between 2007 and 2016, theMoon shadow is observed with 3.5s statistical significance. The detector angular resolution for downwardgoing muons is 0.73. +/- 0.14.. The resulting pointing performance is consistent with the expectations. An independent check of the telescope pointing accuracy is realised with the data collected by a shower array detector onboard of a ship temporarily moving around the ANTARES location.
We consider the process of muon-electron elastic scattering, which has been proposed as an ideal framework to measure the running of the electromagnetic coupling constant at space-like momenta and determine the leading-order hadronic contribution to the muon g-2 (MUonE experiment). We compute the next-to-leading (NLO) contributions due to QED and purely weak corrections and implement them into a fully differential Monte Carlo event generator, which is available for first experimental studies. We show representative phenomenological results of interest for the MUonE experiment and examine in detail the impact of the various sources of radiative corrections under different selection criteria, in order to study the dependence of the NLO contributions on the applied cuts. The study represents the first step towards the realisation of a high-precision Monte Carlo code necessary for data analysis.
The ANTARES neutrino telescope has an energy threshold of a few tens of GeV. This allows to study the phenomenon of atmospheric muon neutrino disappearance due to neutrino oscillations. In a similar way, constraints on the 3+1 neutrino model, which foresees the existence of one sterile neutrino, can be inferred. Using data collected by the ANTARES neutrino telescope from 2007 to 2016, a new measurement of m 2 and (23) has been performed which is consistent with world best-fit values and constraints on the 3+1 neutrino model have been derived.
We consider the computation of volumes contained in a spatial slice of AdS(3) in terms of observables in a dual CFT. Our main tool is kinematic space, defined either from the bulk perspective as the space of oriented bulk geodesics, or from the CFT perspective as the space of entangling intervals. We give an explicit formula for the volume of a general region in a spatial slice of AdS(3) as an integral over kinematic space. For the region lying below a geodesic, we show how to write this volume purely in terms of entangling entropies in the dual CFT. This expression is perhaps most interesting in light of the complexity = volume proposal, which posits that complexity of holographic quantum states is computed by bulk volumes. An extension of this idea proposes that the holographic subregion complexity of an interval, defined as the volume under its Ryu-Takayanagi surface, is a measure of the complexity of the corresponding reduced density matrix. If this is true, our results give an explicit relationship between entanglement and subregion complexity in CFT, at least in the vacuum. We further extend many of our results to conical defect and BTZ black hole geometries.
KM3NeT will be a network of deep-sea neutrino telescopes in the Mediterranean Sea. The KM3NeT/ARCA detector, to be installed at the Capo Passero site (Italy), is optimised for the detection of high-energy neutrinos of cosmic origin. Thanks to its geographical location on the Northern hemisphere, KM3NeT/ARCA can observe upgoing neutrinos from most of the Galactic Plane, including the Galactic Centre. Given its effective area and excellent pointing resolution, KM3NeT/ARCA will measure or significantly constrain the neutrino flux from potential astrophysical neutrino sources. At the same time, it will test flux predictions based on gamma-ray measurements and the assumption that the gamma-ray flux is of hadronic origin. Assuming this scenario, discovery potentials and sensitivities for a selected list of Galactic sources and to generic point sources with an E-2 spectrum are presented. These spectra are assumed to be time independent. The results indicate that an observation with 3 sigma significance is possible in about six years of operation for the most intense sources, such as Supernovae Remnants RX J1713.7-3946 and Vela Jr. If no signal will be found during this time, the fraction of the gamma-ray flux coming from hadronic processes can be constrained to be below 50% for these two objects. (C) 2019 The Authors. Published by Elsevier B.V.
In this thesis we discuss the potential of nanodevices based on topological insulators. This novel class of matter is characterized by an insulating bulk with simultaneously conducting boundaries. To lowest order, the states that are evoking the conducting behavior in TIs are typically described by a Dirac theory. In the two-dimensional case, together with time- reversal symmetry, this implies a helical nature of respective states. Then, interesting physics appears when two such helical edge state pairs are brought close together in a two-dimensional topological insulator quantum constriction. This has several advantages. Inside the constriction, the system obeys essentially the same number of fermionic fields as a conventional quantum wire, however, it possesses more symmetries. Moreover, such a constriction can be naturally contacted by helical probes, which eventually allows spin- resolved transport measurements.
We use these intriguing properties of such devices to predict the formation and detection of several profound physical effects. We demonstrate that narrow trenches in quantum spin Hall materials – a structure we coin anti-wire – are able to show a topological super- conducting phase, hosting isolated non-Abelian Majorana modes. They can be detected by means of a simple conductance experiment using a weak coupling to passing by helical edge states. The presence of Majorana modes implies the formation of unconventional odd-frequency superconductivity. Interestingly, however, we find that regardless of the presence or absence of Majoranas, related (superconducting) devices possess an uncon- ventional odd-frequency superconducting pairing component, which can be associated to a particular transport channel. Eventually, this enables us to prove the existence of odd- frequency pairing in superconducting quantum spin Hall quantum constrictions. The symmetries that are present in quantum spin Hall quantum constrictions play an essen- tial role for many physical effects. As distinguished from quantum wires, quantum spin Hall quantum constrictions additionally possess an inbuilt charge-conjugation symmetry. This can be used to form a non-equilibrium Floquet topological phase in the presence of a time-periodic electro-magnetic field. This non-equilibrium phase is accompanied by topological bound states that are detectable in transport characteristics of the system. Despite single-particle effects, symmetries are particularly important when electronic in- teractions are considered. As such, charge-conjugation symmetry implies the presence of a Dirac point, which in turn enables the formation of interaction induced gaps. Unlike single-particle gaps, interaction induced gaps can lead to large ground state manifolds. In combination with ordinary superconductivity, this eventually evokes exotic non-Abelian anyons beyond the Majorana. In the present case, these interactions gaps can even form in the weakly interacting regime (which is rather untypical), so that the coexistence with superconductivity is no longer contradictory. Eventually this leads to the simultaneous presence of a Z4 parafermion and a Majorana mode bound at interfaces between quantum constrictions and superconducting regions.
Topological superconductors represent a fruitful playing ground for fundamental research as well as for potential applications in fault-tolerant quantum computing. Especially Josephson junctions based on topological superconductors remain intensely studied, both theoretically and experimentally. The characteristic property of these junctions is their 4-periodic ground-state fermion parity in the superconducting phase difference. Using such topological Josephson junctions, we introduce the concept of a topological Josephson heat engine. We discuss how this engine can be implemented as a Josephson-Stirling cycle in topological superconductors, thereby illustrating the potential of the intriguing and fruitful marriage between topology and coherent thermodynamics. It is shown that the Josephson-Stirling cycle constitutes a highly versatile thermodynamic machine with different modes of operation controlled by the cycle temperatures. Finally, the thermodynamic cycle reflects the hallmark 4 pi -periodicity of topological Josephson junctions and could therefore be envisioned as a complementary approach to test topological superconductivity. Topological superconductors are expected to be a key component of quantum computing systems but reliably detecting their exotic properties is a challenge. Here, the authors propose a topological Josephson heat engine which uses thermodynamic effects to probe the 4 pi -periodic ground state of a topological superconductor.
Adding interactions to topological (non-)trivial free fermion systems can in general have four different effects: (i) In symmetry protected topological band insulators, the correlations may lead to the spontaneous breaking of some protecting symmetries by long-range order that gaps the topological boundary modes. (ii) In free fermion (semi-)metal, the interaction could vice versa also generate long-range order that in turn induces a topological mass term and thus generates non-trivial phases dynamically. (iii) Correlation might reduce the topological classification of free fermion systems by allowing adiabatic deformations between states of formerly distinct phases. (iv) Interaction can generate long-range entangled topological order in states such as quantum spin liquids or fractional quantum Hall states that cannot be represented by non-interacting systems. During the course of this thesis, we use numerically exact quantum Monte Carlo algorithms to study various model systems that (potentially) represent one of the four scenarios, respectively.
First, we investigate a two-dimensional $d_{xy}$-wave, spin-singlet superconductor, which is relevant for high-$T_c$ materials such as the cuprates. This model represents nodal topological superconductors and exhibits chiral flat-band edge states that are protected by time-reversal and translational invariance. We introduce the conventional Hubbard interaction along the edge in order to study their stability with respect to correlations and find ferromagnetic order in case of repulsive interaction as well as charge-density-wave order and/or additional $i$s-wave pairing for attractive couplings. A mean-field analysis that, for the first time, is formulated in terms of the Majorana edge modes suggests that any order has normal and superconducting contributions. For example, the ferromagnetic order appears in linear superposition with triplet pairing. This finding is well confirmed by the numerically exact quantum Monte Carlo investigation.
Second, we consider spinless electrons on a two-dimensional Lieb lattice that are subject to nearest-neighbor Coulomb repulsion. The low energy modes of the free fermion part constitute a spin-$1$ Dirac cone that might be gapped by several mass terms. One option breaks time-reversal symmetry and generates a topological Chern insulator, which mainly motivated this study. We employ two flavors of quantum Monte Carlo methods and find instead the formation of charge-density-wave order that breaks particle-hole symmetry. Additionally, due to sublattices of unequal size in Lieb lattices, this induces a finite chemical potential that drives the system away from half-filling. We argue that this mechanism potentially extends the range of solvable models with finite doping by coupling the Lieb lattice to the target system of interest.
Third, we construct a system with four layers of a topological insulators and interlayer correlation that respects one independent time-reversal and a unitary $\mathbb{Z}_2$ symmetry. Previous studies claim a reduced topological classification from $\mathbb{Z}$ to $\mathbb{Z}_4$, for example by gapping out degenerate zero modes in topological defects once the correlation term is designed properly. Our interaction is chosen according to this analysis such that there should exist an adiabatic deformation between states whose topological invariant differs by $\Delta w=\pm4$ in the free fermion classification. We use a projective quantum Monte Carlo algorithm to determine the ground-state phase diagram and find a symmetry breaking regime, in addition to the non-interacting semi-metal, that separates the free fermion insulators. Frustration reduces the size of the long-range ordered region until it is replaced by a first order phase transition. Within the investigated range of parameters, there is no adiabatic path deforming the formerly distinct free fermion states into each other. We conclude that the prescribed reduction rules, which often use the bulk-boundary correspondence, are necessary but not sufficient and require a more careful investigation.
Fourth, we study conduction electron on a honeycomb lattice that form a Dirac semi-metal Kondo coupled to spin-1/2 degrees of freedom on a Kagome lattice. The local moments are described by a variant of the Balents-Fisher-Girvin model that has been shown to host a ferromagnetic phase and a $\mathbb{Z}_2$ spin liquid at strong frustration. Here, we report the first numerical exact quantum Monte Carlo simulation of the Kondo-coupled system that does not exhibit the negative-sign problem. When the local moments form a ferromagnet, the Kondo coupling induces an anti-ferromagnetic mass term in the conduction-electron system. At large frustration, the Dirac cone remains massless and the spin system forms a $\mathbb{Z}_2$ spin liquid. Owing to the odd number of spins per unit cell, this constitutes a non-Fermi liquid that violates Luttinger's theorem which relates the Fermi volume to the particle density in a Fermi liquid. This phase is a specific realization of the so called 'fractional Fermi liquid` as it has been first introduced in the context of heavy fermion models.
In this thesis we consider the hybrid quantum Monte Carlo method for simulations of the Hubbard and Su-Schrieffer-Heeger model. In the first instance, we discuss the hybrid quantum Monte Carlo method for the Hubbard model on a square lattice. We point out potential ergodicity issues and provide a way to circumvent them by a complexification of the method. Furthermore, we compare the efficiency of the hybrid quantum Monte Carlo method with a well established determinantal quantum Monte Carlo method for simulations of the half-filled Hubbard model on square lattices. One reason why the hybrid quantum Monte Carlo method loses the comparison is that we do not observe the desired sub-quadratic scaling of the numerical effort. Afterwards we present a formulation of the hybrid quantum Monte Carlo method for the Su-Schrieffer-Heeger model in two dimensions. Electron-phonon models like this are in general very hard to simulate using other Monte Carlo methods in more than one dimensions. It turns out that the hybrid quantum Monte Carlo method is much better suited for this model . We achieve favorable scaling properties and provide a proof of concept. Subsequently, we use the hybrid quantum Monte Carlo method to investigate the Su-Schrieffer-Heeger model in detail at half-filling in two dimensions. We present numerical data for staggered valence bond order at small phonon frequencies and an antiferromagnetic order at high frequencies. Due to an O(4) symmetry the antiferromagnetic order is connected to a superconducting charge density wave. Considering the Su-Schrieffer-Heeger model without tight-binding hopping reveals an additional unconstrained Z_2 gauge theory. In this case, we find indications for π-fluxes and a possible Z_2 Dirac deconfined phase as well as for a columnar valence bond ordered state at low phonon energies. In our investigations of the several phase transitions we discuss the different possibilities for the underlying mechanisms and reveal first insights into a rich phase diagram.
In this review paper, we stress the importance of the higher transcendental Wright functions of the second kind in the framework of Mathematical Physics. We first start with the analytical properties of the classical Wright functions of which we distinguish two kinds. We then justify the relevance of the Wright functions of the second kind as fundamental solutions of the time-fractional diffusion-wave equations. Indeed, we think that this approach is the most accessible point of view for describing non-Gaussian stochastic processes and the transition from sub-diffusion processes to wave propagation. Through the sections of the text and suitable appendices, we plan to address the reader in this pathway towards the applications of the Wright functions of the second kind.
Background and Objectives
To analyze the impact of humidity and temperature on excimer laser ablation of polyethylene terephthalate (PET), polymethylmethacrylate (PMMA) and porcine corneal tissue, and an ablation model to compensate for the temperature and humidity changes on ablation efficiency.
Study Design/Materials and Methods
The study was conducted using an AMARIS 1050RS (Schwind eye‐tech‐solutions) placed inside a climate chamber at ACTS. Ablations were performed on PET, PMMA, and porcine cornea. The impact of a wide range of temperature (~18°C to ~30°C) and relative humidity (~25% to ~80%) on laser ablation outcomes was tested using nine climate test settings. For porcine eyes, change in defocus was calculated from the difference of post‐ablation to pre‐ablation average keratometry readings. Laser scanning deflectometry was performed to measure refractive change achieved in PMMA. Multiple linear regression was performed using the least square method with predictive factors: temperature, relative humidity, time stamp. Influence of climate settings was modeled for pulse energy, pulse fluence, ablation efficiency on PMMA and porcine cornea tissue.
Results
Temperature changes did not affect laser pulse energy, pulse fluence (PET), and ablation efficiency (on PMMA or porcine corneal tissue) significantly. Changes in relative humidity were critical and significantly affected laser pulse energy, high fluence and low fluence. The opposite trend was observed between the ablation performance on PMMA and porcine cornea.
Conclusions
The proposed well‐fitting multi‐linear model can be utilized for compensation of temperature and humidity changes on ablation efficiency. Based on this model, a working window for optimum operation has been found (temperature 18°C to 28°C and relative humidity 25% to 65%) for a maximum deviation of ±2.5% in ablation efficiency in PMMA and porcine corneal tissue.