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- Institut für Theoretische Physik und Astrophysik (122) (remove)
Sonstige beteiligte Institutionen
At the beginning of regular observations with the MAGIC telescope in December 2004, all but one extragalactic sources detected at very high energy (VHE) gamma-rays belonged to the class of high frequency peaked BL Lac (HBL) objects. This motivated a systematic scan of candidate sources to increase the number of known sources and to study systematically their spectral properties. As candidate sources for VHE emission, X-ray bright HBLs were selected from a compilation of active galactic nuclei. The MAGIC observations took place from December 2004 to March 2006. The declination of the objects was restricted to values between -1.2° and +58.8° corresponding to a maximum zenith distance lower than 30° at culmination. Since gamma-rays are absorbed by photo-pair production in low energy background radiation fields, the redshift of the investigated objects was limitetd to z < 0.3. Under the assumption that HBLs generally emit the same energy flux at 1keV as at 200GeV, only the brightest X-ray sources were observed, leading to a cut in the X-ray flux of F(1keV) > 2µJy}. Of the fourteen sources observed, four have been detected: 1ES 1218+304 (for the first time at very high energies), 1ES 2344+514 (strong detection in a state of low activity), Mrk 421 and Mrk 501. A hint of a signal on a 3-sigma-level from the direction of 1ES 1011+496 has been observed. In the meantime the object has been confirmed as a source of VHE gamma-rays by a second MAGIC observation campaign triggered by an optical outburst. For ten sources, upper limits on their integral fluxes above 200GeV have been calculated on a 99% confidence level. To cross calibrate the different data samples, collected during 14 months, bright muon ring images have been used, recorded as background events by the MAGIC telescope. Based on the development by Meyer (2003), the method has been improved and implemented into the automatic data analysis as a continuous monitor of the calibration and the point spread function of the optical system. While the ring images are generated by muons with small impact parameters, it could be shown that the image parameter distributions for muons with large impact parameters and gamma showers completely overlap, revealing these muons as the dominant background for gamma-ray observations below energies of 150GeV. The sample of HBLs (including all HBLs detected at VHE so far) has been investigated for correlations between broad-band spectral indices as determined from simultaneous optical, archival X-ray and radio luminosities, finding that the VHE emitting HBLs do not differ from the non-detected ones. In general the absorption corrected HBL gamma-ray luminosities at 200GeV are not higher than their X-ray luminosities at 1keV. Based on a complete X-ray BL Lac sample, the Hamburg/ROSAT X-ray BL Lac sample, the number of expected VHE sources has been estimated for the performed scan, finding a consistent number under the assumption of a 37% completeness of the investigated sample and a 1keV-to-200GeV luminosity ratio of 1.4. An upper limit on the omnidirectional flux at 200GeV has been calculated by interpolating the sum over the observed fluxes and upper limits. Within the uncertainties, the result is in agreement with the expectations derived from the X-ray luminosity function of BL Lacs. For 1ES 1218+304 and 1ES 2344+514 the lightcurves have been derived, showing evidence for flux variability on a time scale of 17 days and 24h, respectively. In the case of 1ES 1218+304 variability has been reported for the first time at VHEs. For both sources the energy spectra have been reconstructed and discussed in the context of their broad band spectral energy distribution (SED), using a single zone synchrotron self Compton model. The SEDs are well fitted by the simulation even though the very high peak frequencies at gamma-rays push the model to its limits. The parameters derived from the simulation are in good agreement with the parameters found for similar HBLs.
In this PhD thesis, the effect of strain on heteroepitaxial growth is investigated by means of Kinetic Monte Carlo simulations. In this context the lattice misfit, arising from the different lattice constants of the adsorbate and the substrate material, is of particular interest. As a consequence, this lattice misfit leads to long-range elastic strain effects having strong influence on the entire growing crystal and its resulting surface morphology. The main focus of this work is the investigation of different strain relaxation mechanisms and their controlling parameters, revealing interesting consequences on the subsequent growth. Since epitaxial growth is carried out under conditions far away from thermodynamic equilibrium, it is strongly determined by surface kinetics. At this point the relevant kinetic microscopic processes are described, followed by theoretical considerations of heteroepitaxial growth disclosing an overview over several independent methodological streams, used to model epitaxy in different time and length scales, as well as the characterization of misfit dislocations and the classification of epitaxial growth modes based on thermodynamic considerations. The epitaxial growth is performed by means of Kinetic Monte Carlo simulations which allows for the consideration of long range effects in systems with lateral extension of few hundred atoms. By using an off-lattice simulation model the particles are able to leave their predefined lattice sites, which is an indispensable condition for simulating strain relaxation mechanisms. The main idea of our used model is calculating the activation energy of all relevant thermally activated processes by using simple pair potentials and then realizing the dynamics by performing each event according to its probability by means of a rejection-free algorithm method. In addition, the crystal relaxation procedure, the grid-based particle access method, which accelerates the simulation enormously, and the efficient implementation of the algorithm are discussed. To study the influence of long range elastic strain effects, the main part of this work was realized on the two dimensional triangular lattice, which can be treated as a cross section of the real three dimensional case. Chapter 4 deals with the formation of misfit dislocations as a strain relaxation mechanism and the resulting consequences on the subsequent heteroepitaxial growth. We can distinguish between two principally different dislocation formation mechanisms, depending strongly on the sign as well as on the magnitude of the misfit, but also the surface kinetics need to be taken into account. Additionally, the dislocations affect the lattice spacings of the crystal whose observed progression is in qualitative good agreement with experimental results. Furthermore, the dislocations influence the subsequent growth of the adsorbate film, since the potential energy of an adatom is modulated by buried dislocations. A clear correlation between the lateral positions of buried dislocations and the positions of mounds grown on the surface can be observed. In chapter 5, an alternative strain relaxation mechanism is studied: the formation of three dimensional islands enables the particles to approach their preferred lattice spacing. We demonstrate that it is possible to adjust within our simulation model each of the three epitaxial growth modes: Volmer–Weber, Frank–van der Merve or layer-by-layer, and Stranski–Krastanov growth mode. Moreover, we can show that the emerging growth mode depends in principle on two parameters: on the one hand the interaction strength of adsorbate particles with each other, compared to the interaction of adsorbate with substrate particles, and on the other hand the lattice misfit between adsorbate and substrate particles. A sensible choice of these two parameters allows the realization of each growth mode within the simulations. In conclusion, the formation of nanostructures controlled by an underlying dislocation network can be applied in the concept of self-organized pattern formation as well as by the tendency to form ordered arrays of strain-induced three dimensional grown islands. In chapter 6, we extend our model to three dimensions and investigate the effect of strain on growth on bcc(100) surfaces. We introduce an anisotropic potential yielding a stable bcc lattice structure within the off-lattice representation. We can show that the strain built up in submonolayer islands is mainly released at the island edges and the lattice misfit has strong influence on the diffusion process on the plane surface as well as on the situation at island edges with eminent consequences on the appearance of submonolayer islands.
In this PhD thesis, we study the heteroepitaxial crystal growth by means of Monte Carlo simulations. Of particular interest in this work is the influence of the lattice mismatch of the adsorbates relative to the substrate on surface structures. In the framework of an off-lattice model, we consider one monolayer of adsorbate and investigate the emerging nanopatterns in equilibrium and their formation during growth. In chapter 1, a brief introduction is given, which describes the role of computer simulations in the field of the physics of condensed matter. Chapter 2 is devoted to some technical basics of experimental methods of molecular beam epitaxy and the theoretical description. Before a model for the simulation can be designed, it is necessary to make some considerations of the single processes which occur during epitaxial growth. For that purpose we look at an experimental setup and extract the main microscopic processes. Afterwards a brief overview of different theoretical concepts describing that physical procedures is given. In chapter 3, the model used in the simulations is presented. The aim is to investigate the growth of an fcc crystal in the [111] direction. In order to keep the simulation times within a feasible limit a simple pair potential, the Lennard-Jones potential, with continuous particle positions is used, which are necessary to describe effects resulting from the atomic mismatch in the crystal. Furthermore the detailed algorithm is introduced which is based on the idea to calculate the barrier of each diffusion event and to use the barriers in a rejection-free method. Chapter 4 is attended to the simulation of equilibrium. The influence of different parameters on the emerging structures in the first monolayer upon the surface, which is completely covered with two adsorbate materials, is studied. Especially the competition between binding energy and strain leads to very interesting pattern formations like islands or stripes. In chapter 5 the results of growth simulations are presented. At first, we introduce a model in order to realize off-lattice Kinetic Monte Carlo simulations. Since the costs in simulation time are enormous, some simplifications in the calculation of diffusion barriers are necessary and therefore the previous model is supplemented with some elements from the so-called ball and spring model. The next point is devoted to the calculation of energy barriers followed by the presentation of the growth simulations. Binary systems with only one sort of adsorbate are investigated as well as ternary systems with two different adsorbates. Finally, a comparison to the equilibrium simulations is drawn. Chapter 6 contains some concluding remarks and gives an outlook to possible further investigations.
Calculations of multi-particle processes at the one-loop level: precise predictions for the LHC
(2007)
The Standard Model (SM) of elementary particle physics provides a uniform framework for the description of three fundamental forces, the electromagnetic and weak forces, describing interactions between quarks and leptons, and the strong force, describing a much stronger interaction between the coloured quarks. Numerous experimental tests have been performed in the last thirty years, showing a spectacular agreement with the theoretical predictions of the Standard Model, even at the per mille level, therefore validating the model at the quantum level. An important cornerstone of the Standard Model is the Higgs mechanism, which provides a possible explanation of electroweak symmetry breaking, responsible for the masses of elementary fermions and the W and Z bosons, the carriers of the weak force. This mechanism predicts a scalar boson, the Higgs boson, which has escaped its discovery so far. If the Higgs mechanism is indeed realised in nature, the upcoming Large Hadron Collider (LHC) at CERN will be able to find the associated Higgs boson. The discovery of a Higgs boson by itself is not sufficient to establish the Higgs mechanism, the basic ingredient being the Higgs potential which predicts trilinear and quartic couplings. These have to be confirmed experimentally by the study of multi-Higgs production. We therefore present a calculation of the loop-induced processes gg to HH and gg to HHH, and investigate the observability of multi-Higgs boson production at the LHC in the Standard Model and beyond. While the SM cross sections are too small to allow observation at the LHC, we demonstrate that physics beyond the SM can lead to amplified, observable cross sections. Furthermore, the applicability of the heavy top quark approximation in two- and three-Higgs boson production is investigated. We conclude that multi-Higgs boson production at the SuperLHC is an interesting probe of Higgs sectors beyond the SM and warrants further study. Despite the great success of the SM, it is widely believed that this model cannot be valid for arbitrarily high energies. The LHC will probe the TeV scale and theoretical arguments indicate the appearance of physics beyond the SM at this scale. The search for new physics requires a precise understanding of the SM. Precise theoretical predictions are needed which match the accuracy of the experiments. For the LHC, most analyses require next-to-leading order (NLO) precision. Only then will we be able to reliably verify or falsify different models. At the LHC, many interesting signatures involve more than two particles in the final state. Precise theoretical predictions for such multi-leg processes are a highly nontrivial task and new efficient methods have to be applied. The calculation of the process PP to VV+jet at NLO is an important background process to Higgs production in association with a jet at the LHC. We compute the virtual corrections to this process which form the "bottleneck" for obtaining a complete NLO prediction. The resulting analytic expressions are generated with highly automated computer routines and translated into a flexible Fortran code, which can be employed in the computation of differential cross sections of phenomenological interest. The obtained results for the virtual corrections indicate that the QCD corrections are sizable and should be taken into account in experimental studies for the LHC.
In a first part the bilayer Heisenberg Model and the 2D Kondo necklace model are studied. Both models exhibit a quantum phase transition between an ordered and disordered phase. The question is addressed to the coupling of a single doped hole to the critical fluctuations. A self-consistent Born approximation predicts that the doped hole couples to the magnons such that the quasiparticle residue vanishes at the quantum critical point. In this work the delicate question about the fate of the quasiparticle residue across the quantum phase transition is also tackled by means of large scale quantum Monte Carlo simulations. Furthermore the dynamics of a single hole doped in the magnetic background is investigated. In the second part an analysis of the spiral staircase Heisenberg ladder is presented. The ladder consists of two ferromagnetic coupled spin-1/2 chains, where the coupling within the second chain can be tuned by twisting the ladder. Within this model the crossover between an ungapped spin-1/2 system and a gapped spin-1 system can be studied. In this work the emphasis is on the opening of the spin gap with respect to the ferromagnetic rung coupling. It is shown that there are essential differences in the scaling behavior of the spin gap depending on the twist of the model. Moreover, by means of the string order parameter it is shown, that the system remains in the Haldane phase within the whole parameter range although the spin gap scales differently. The tools which are used for the analyses are mainly large scale quantum Monte Carlo methods, but also exact diagonalization techniques as well as mean field approaches.
Despite its precise agreement with the experiment, the validity of the standard model (SM) of elementary particle physics is ensured only up to a scale of several hundred GeV so far. Even more, the inclusion of gravity into an unifying theory poses a problem which cannot be solved by ordinary quantum field theory (QFT). String theory, which is the most popular ansatz for a unified theory, predicts QFT on noncommutative space-time as a low energy limit. Nevertheless, independently of the motivation given by string theory, the nonlocality inherent to noncommutative QFT opens up the possibility for the inclusion of gravity. There are no theoretical predictions for the energy scale Lambda_NC at which noncommutative effects arise and it can be assumed to lie in the TeV range, which is the energy range probed by the next generation of colliders. Within this work we study the phenomenological consequences of a possible realization of QFT on noncommutative space-time relying on this assumption. The motivation for this thesis was given by the gap in the range of phenomenological studies of noncommutative effects in collider experiments, due to the absence in the literature of Large Hadron Collider (LHC) studies regarding noncommutative QFTs. In the first part we thus performed a phenomenological analysis of the hadronic process pp -> Z gamma -> l^+l^- gamma at the LHC and of electron-positron pair annihilation into a Z boson and a photon at the International Linear Collider (ILC). The noncommutative extension of the SM considered within this work relies on two building blocks: the Moyal-Weyl star-product of functions on ordinary space-time and the Seiberg-Witten maps. The latter relate the ordinary fields and parameters to their noncommutative counterparts such that ordinary gauge transformations induce noncommutative gauge transformations. This requirement is expressed by a set of inhomogeneous differential equations (the gauge equivalence equations) which are solved by the Seiberg-Witten maps order by order in the noncommutative parameter Theta. Thus, by means of the Moyal-Weyl star-product and the Seiberg-Witten maps a noncommutative extension of the SM as an effective theory as expansion in powers of Theta can be achieved, providing the framework of our phenomenological studies. A consequence of the noncommutativity of space-time is the violation of rotational invariance with respect to the beam axis. This effect shows up in the azimuthal dependence of cross sections, which is absent in the SM as well as in other models beyond the SM. Thus, the azimuthal dependence of the cross section is a typical signature of noncommutativity and can be used in order to discriminate it against other new physics effects. We have found this dependence to be best suited for deriving the sensitivity bounds on the noncommutative scale Lambda_NC. By studying pp -> Z gamma -> l^+l^- gamma to first order in the noncommutative parameter Theta, we show in the first part of this work that measurements at the LHC are sensitive to noncommutative effects only in certain cases, giving bounds on the noncommutative scale of Lambda_NC > 1.2 TeV. Our result improved the bounds present in the literature coming from past and present collider experiments by one order of magnitude. In order to explore the whole parameter range of the noncommutativity, ILC studies are required. By means of e^+e^- -> Z gamma -> l^+l^- gamma to first order in Theta we have shown that ILC measurements are complementary to LHC measurements of the noncommutative parameters. In addition, the bounds on Lambda_NC derived from the ILC are significantly higher and reach Lambda_NC > 6 TeV. The second part of this work arose from the necessity to enlarge the range of validity of our model towards higher energies. Thus, we expand the neutral current sector of the noncommutative SM to second order in $\theta$. We found that, against the general expectation, the theory must be enlarged by additional parameters. The new parameters enter the theory as ambiguities of the Seiberg-Witten maps. The latter are not uniquely determined and differ by homogeneous solutions of the gauge equivalence equations. The expectation was that the ambiguities correspond to field redefinitions and therefore should vanish in scattering matrix elements. However, we proved that this is not the case, and the ambiguities do affect physical observables. Our conjecture is, that every order in Theta will introduce new parameters to the theory. However, only the experiment can decide to what extent efforts with still higher orders in Theta are reasonable and will also give directions for the development of theoretical models of noncommutative QFTs.
Neural networks can synchronize by learning from each other. For that purpose they receive common inputs and exchange their outputs. Adjusting discrete weights according to a suitable learning rule then leads to full synchronization in a finite number of steps. It is also possible to train additional neural networks by using the inputs and outputs generated during this process as examples. Several algorithms for both tasks are presented and analyzed. In the case of Tree Parity Machines the dynamics of both processes is driven by attractive and repulsive stochastic forces. Thus it can be described well by models based on random walks, which represent either the weights themselves or order parameters of their distribution. However, synchronization is much faster than learning. This effect is caused by different frequencies of attractive and repulsive steps, as only neural networks interacting with each other are able to skip unsuitable inputs. Scaling laws for the number of steps needed for full synchronization and successful learning are derived using analytical models. They indicate that the difference between both processes can be controlled by changing the synaptic depth. In the case of bidirectional interaction the synchronization time increases proportional to the square of this parameter, but it grows exponentially, if information is transmitted in one direction only. Because of this effect neural synchronization can be used to construct a cryptographic key-exchange protocol. Here the partners benefit from mutual interaction, so that a passive attacker is usually unable to learn the generated key in time. The success probabilities of different attack methods are determined by numerical simulations and scaling laws are derived from the data. If the synaptic depth is increased, the complexity of a successful attack grows exponentially, but there is only a polynomial increase of the effort needed to generate a key. Therefore the partners can reach any desired level of security by choosing suitable parameters. In addition, the entropy of the weight distribution is used to determine the effective number of keys, which are generated in different runs of the key-exchange protocol using the same sequence of input vectors. If the common random inputs are replaced with queries, synchronization is possible, too. However, the partners have more control over the difficulty of the key exchange and the attacks. Therefore they can improve the security without increasing the average synchronization time.
The basic question which drove our whole work was to find a meaningful noncommutative gauge theory even for the time-like case ($\theta^{0 i} \neq 0$). In order to be able to tackle questions regarding unitarity, it is not sufficient to consider theories which include the noncommutative parameter only up to a finite order. The reason is that in order to investigate tree-level unitarity or the optical theorem in loops one has to know the behavior of the noncommutative theory for center-of-mass energies much greater than the noncommutative scale. Therefore an effective theory, that is by construction only valid up to the noncommutative scale, isn't sufficient for our purpose. Our model is based on two fundamental assumptions. The first assumption is given by the commutation relations \eqref{eq:ncalg}. This led to the Moyal-Weyl star-product \eqref{eq:astproduct2} which replaces all point-like products between two fields. The second assumption is to assume that the model built this way is not only invariant under the noncommutative gauge transformation but also under the commutative one. In order to obtain an action of such a model one has to replace the fields by their appropriate \swms. We chose the gauge fixed action \eqref{eq:actioncgf} as the fundamental action of our model. After having constructed the action of the NCQED including the {\swms} we were confronted with the problem of calculating the {\swms} to all orders in $\tMN$. By means of \cite{bbg} we could calculate the {\swms} order by order in the gauge field, where each order in the gauge field contains all orders in the noncommutative parameter (\cf chapter \ref{chapter:swms}). By comparing the maps with the result we obtained from an alternative ansatz \cite{bcpvz}, we realized that already the simplest {\swm} for the gauge field is not unique. In chapter \ref{chapter:ambiguities} we examined this ambiguity, which we could parametrised by an arbitrary function $\astf$. The next step was to derive the Feynman rules for our NCQED. One finds that the propagators remain unchanged so that the free theory is equal to the commutative QED. The fermion-fermion-photon vertex contains not only a phase factor coming from the Moyal-Weyl star-product but also two additional terms which have their origin in the \swms. Beside the 3-photon vertex which is already present in NCQED without {\swms} and which has also additional terms coming from the \swms, too, one has a contact vertex which couples two fermions with two photons. After having derived all the vertices we calculated the pair annihilation scattering process $e^+ e^- \rightarrow \gamma \gamma$ at Born level. By choosing the parameter $\kggg = 1$ (\cf section \ref{sec:represent}), we found that the amplitude of the pair annihilation process becomes equal to the amplitude of the NCQED without \swms. This means that, at least for this process, the NCQED excluding {\swms} is only a special case of NCQED including \swms. On the basis of the pair annihilation process, we afterwards investigated tree-level unitarity. In order to satisfy the tree-level unitarity we had to constrain the arbitrary function $\astf$. We found that the series expansion of $\astf$ has to start with unity. In addition, the even part of the function must not increase faster than $s^{-1/2} \log(s)$ for $s \rightarrow \infty$, whereas the odd part of the $\astf$-function can't be constrained, at least by the process we considered. By assuming these constrains for the $\astf$-function, we could show that tree-level unitarity is satisfied if one incorporates the uncertainties present in the energy and the momenta of the scattered particles, \ie the uncertainties of the center-of-mass energy and the scattering angles. This uncertainties are not exclusively present due to the finite experimental resolution. A delta-like center-of-mass energy as well as delta-like momenta are in general not possible because the scattered particles are never exact plane waves.
The astronomical exploration at energies between 30\,GeV and $\lesssim$\,350\,GeV was the main motivation for building the \MAGIC-telescope. With its 17\,m \diameter\ mirror it is the worldwide largest imaging air-Cherenkov telescope. It is located at the Roque de los Muchachos at the Canary island of San Miguel de La Palma at 28.8$^\circ$\,N, 17.8$^\circ$\,W, 2200\,m a.s.l. The telescope detects Cherenkov light produced by relativistic electrons and positrons in air showers initiated by cosmic gamma-rays. The imaging technique is used to powerfully reject the background due to hadronically induced air showers from cosmic rays. Their inverse power-law energy-distribution leads to an increase of the event rate with decreasing energy threshold. For \MAGIC this implies a trigger rate in the order of 250\,Hz, and a correspondingly large data stream to be recorded and analyzed. A robust analysis software package, including the general framework \MARS, was developed and commissioned to allow automation, necessary for data taken under variable observing conditions. Since many of the astronomical sources of high-energy radiation, in particular the enigmatic gamma-ray bursts, are of a transient nature, the telescope was designed to allow repositioning in several tens of seconds, keeping a tracking accuracy of $\lesssim\,$0.01$^\circ$. Employing a starguider, a tracking accuracy of $\lesssim\,$1.3\,minutes of arc was obtained. The main class of sources at very high gamma-ray energies, known from previous imaging air-Cherenkov telescopes, are Active Galactic Nuclei with relativistic jets, the so-called high-peaked Blazars. Their spectrum is entirely dominated by non-thermal emission, spanning more than 15 orders of magnitude in energy, from radio to gamma-ray energies. Predictions based on radiation models invoking a synchrotron self-Compton or hadronic origin of the gamma-rays suggest, that a fairly large number of them should be detectable by \MAGIC. Promising candidates have been chosen from existing compilations, requiring high (synchrotron) X-ray flux, assumed to be related to a high (possibly inverse-Compton) flux at GeV energies, and a low distance, in oder to avoid strong attenuation due to pair-production in interactions with low-energy photons from the extragalactic background radiation along the line of sight. Based on this selection the first \AGN, emitting gamma-rays at 100\,GeV, 1ES\,1218+304 at a redshift of $z=0.182$, was discovered, one of the two farthest known \AGN emitting in the TeV energy region. In this context, the automated analysis chain was successfully demonstrated. The source was observed in January 2005 during six moonless nights for 8.2\,h. At the same time the collaborating \KVA-telescope, located near the \MAGIC site, observed in the optical band. The lightcurve calculated showed no day-to-day variability and is compatible with a constant flux of $F($\,$>$\,$100\,\mbox{GeV})=(8.7\pm1.4) \cdot 10^{-7}\,\mbox{m}^{-2}\,\mbox{s}^{-1}$ within the statistical errors. A differential spectrum between 87\,GeV and 630\,GeV was calculated and is compatible with a power law of $F_E(E) = (8.1\pm 2.1) \cdot 10^{-7}(E/\mbox{250\,GeV})^{-3.0\pm0.4}\,\mbox{TeV}^{-1}\,\mbox{m}^{-2}\,\mbox{s}^{-1}$ within the statistical errors. The spectrum emitted by the source was obtained by taking into account the attenuation due to pair-production with photons of the extragalactic background at low photon energies. A homogeneous, one-zone synchrotron self-Compton model has been fitted to the collected multi-wavelength data. Using the simultaneous optical data, a best fit model could be obtained from which some physical properties of the emitting plasma could be inferred. The result was compared with the so-called {\em Blazar sequence}.
The mechanism of spontaneous symmetry breaking is essential to provide masses to the W and Z gauge bosons and fermions of the SM. We hope to elucidate this mechanism at the next generation of colliders. While the SM has been tested with astonishing precision it is believed to be an effective theory of a more fundamental Great Unified Theory. SUSY is one of the most attractive extensions of the SM of particle physics. Therefore, the search for SUSY is a top priority at the next generation of colliders. Once Higgs bosons are discovered, a precise determination of their properties is necessary to differentiate between different models, in particular the MSSM. A muon collider, running at center of mass energies around the neutral Higgs boson resonances, would allow precise measurements of masses and widths, as well as the couplings to their decay products. In particular their couplings to supersymmetric particles are essential to probe SUSY. Therefore, we study the decays of the heavier CP-even and CP-odd Higgs bosons into lighter chargino or neutralino pairs. In this thesis we have analyzed the polarization effects of the beams and the charginos and neutralinos produced in mu+ mu- annihilation around the center of mass energies of the Higgs boson resonances H and A. For the production of equal charginos we have shown that the ratio of H-chargino and A-chargino couplings can be precisely determined independently of the chargino decay mechanism. This method avoids reference to other experiments and makes only a few model-dependent assumptions. Here we have analyzed the effect of the energy spread and of the error from the non-resonant channels, including an irreducible standard model background contribution. For small tan(beta) the process yields large cross sections of up to a pb. For the production of two different charginos we have shown that the H-A interference can be analyzed using asymmetries of the charge conjugated processes. The asymmetries depend on the muon longitudinal beam polarizations and vanish for unpolarized beams. For the chargino pair production with subsequent two-body decay of one of the charginos we have shown that charge and beam polarization asymmetries in the energy distributions of the decay particles are sensitive to the interference of scalar exchange channels with different CP quantum numbers. This process provides unique information on the interference of overlapping Higgs boson resonances. The effect is larger for regions of parameter space with intermediate values of tan(beta) and light sleptons or LSP neutralinos. For the chargino pair production with subsequent two-body decays of both charginos we have defined energy distribution and angular asymmetries in the final particles, in order to analyze the spin-spin correlations of the charginos. The transverse polarizations of the charginos are sensitive to the CP quantum number of the exchanged Higgs bosons and can thus be used to separate overlapping resonances, as well as to determine the CP quantum number of a single resonance. For equal charginos, these asymmetries are not sensitive to the interference of CP-even and CP-odd Higgs exchange channels. For the neutralino pair production in mu+ mu- annihilation we study similar processes as for chargino production. Line shape measurements of neutralino pair production allow to precisely determine the ratio of H-neutralino and A-neutralino couplings. Neutralino pair production with subsequent two-body decay of one of the neutralinos in the intermediate tan(beta) region is sensitive to the interference of H and A and may be measured with a large statistical significance. The Majorana nature of the neutralinos implies that the beam polarization asymmetries vanish for the remaining production channels. For neutralino pair production with subsequent two-body decays of both neutralinos we analyze similar observables as in chargino production. The main difference consists in the intrinsic relative CP quantum number of the neutralino pair, which depends on the chosen scenario. We have thus shown that the interaction of the Higgs bosons to the gaugino-higgsino sector can be probed at a muon collider in chargino and neutralino pair production, both analyzing the production line-shape around the resonances as well as studying the chargino and neutralino polarizations via their decays.
Diese Arbeit wurde durch Experimente zur Potential- und Stromverteilung in Quanten-Hall- Systemen motiviert, die in den letzten Jahren in der Abteilung von Klitzing am MPI für Festkörperforschung durchgeführt wurden und ergaben, dass elektrostatische Abschirmungseffekte in zweidimensionalen Elektronensystemen (2DES), die den ganzzahligen Quanten-Hall-Effekt (QHE) zeigen, sehr wichtig für das Verständnis der Stromverteilung innerhalb der Probe und der extremen Genauigkeit der gemessenen quantisierten Werte des Hall-Widerstands sind. Daraus ergab sich für die hier vorgelegte Arbeit das folgende Programm. Zunächst wird, nach einem einleitenden Kapitel, in Kapitel 2 der Formalismus vorgestellt, mit dem in den späteren Kapiteln Elektronendichten und elektrostatische Potentiale, die z.B. das 2DES auf eine Probe mit Streifengeometrie eingrenzen, selbstkonsistent berechnet werden. Diese Selbstkonsistenz besteht aus zwei Teilen. Erstens wird, bei vorgegebenem Potential, die Elektronendichte berechnet. Zweitens wird aus vorgegebener Ladungsverteilung, bestehend aus (positiven) Hintergrundladungen und der (im ersten Schritt berechneten) Elektronenladungsdichte, und geeigneten Randbedingungen (konstantes Potential auf metallischen Gates) durch Lösen der Poisson-Gleichung das elektrostatische Potential berechnet. Wenn wir im ersten Schritt, unter Berücksichtigung der Fermi-Dirac-Statistik, die Elektronendichte quantenmechanisch aus den Energieeigenfunktionen und -werten berechnen, erhalten wir die Hartree-Näherung, die die Dichte als nichtlokales Funktional des Potentials liefert. Wenn man die Ausdehnung der Wellenfunktionen auf der Längenskala, auf der sich das Potential typischerweise ändert, vernachlässigen kann, so vereinfacht sich die Hartree-Näherung zur Thomas- Fermi-Näherung, die einen lokalen Zusammenhang zwischen Elektronendichte und Potential beschreibt. Die meisten der konkreten Rechnungen wurden im Rahmen dieser selbstkonsistenten Thomas-Fermi-Poisson-Näherung durchgeführt. Im Kapitel 3 wird allgemein das Abschirmverhalten eines 2DES im hohen Magnetfeld untersucht. Wir betrachten die Antwort auf eine harmonische Potentialmodulation im unbegrenzten 2DES und in streifenförmig begrenzten Systemen mit zwei unterschiedlichen Arten von Randbedingungen. Bei tiefen Temperaturen und hohen Magnetfeldern finden wir extrem nichtlineare Abschirmung. Im unbegrenzten 2DES charakterisieren wir die Abschirmung, indem wir die gesamte Variation des selbstkonsistent berechneten Potentials als Funktion der Amplitude des aufgeprägten cosinus-Potentials berechnen. Bei festem Magnetfeld ergeben sich so Stufenfunktionen, deren Gestalt stark vom Füllfaktor der Landau-Niveaus im homogenen Zustand ohne aufgeprägtes Potential abhängt (siehe Abbildungen 3.2- 3.6). Vielleicht noch unerwartetere Kurven ergeben sich, wenn man bei festem Modulationspotential die Varianz des selbstkonsistenten Potentials gegen das Magnetfeld B aufträgt (Abb. 3.9). Die Resultate lassen sich aber leicht verstehen und (bei Temperatur T = 0) in einem einfachen Schema (Abb. 3.7) zusammenfassen. Als ordnendes Prinzip stellt sich heraus, dass sich stets Zustände einstellen, in denen die Elektronendichte möglichst wenig von der bei verschwindendem Magnetfeld abweicht. Wenn die Zyklotronenergie groß gegen die thermische Energie kBT ist, erfordert das, dass in den großen Bereichen, in denen die Dichte variiert, ein Landau-Niveau unmittelbar an dem, im Gleichgewicht konstanten, elektrochemischen Potential liegen muss (En, “pinning”). Man nennt diese Bereiche kompressibel. In den kompressiblen Bereichen können Elektronen leicht umverteilt werden, d.h. die Dichte ist leicht veränderbar und in diesen Bereichen gibt es extrem effektive Abschirmung. Existieren kompressible Bereiche mit unterschiedlichen Landau-Niveaus (En) am elektrochemischen Potential, z.B. bei großer Modulation oder weil die Dichte zum Probenrand hin abnimmt, so gibt es zwischen benachbarten kompressiblen Bereichen mit unterschiedlichen Landau-Quantenzahlen n “inkompressible” Bereiche, in denen zwischen zwei Landau-Niveaus liegt. Dort sind alle Landau-Niveaus unterhalb von besetzt, die oberhalb leer. Folglich ist dort der Füllfaktor ganzzahlig und die Dichte konstant. Das Wechselspiel zwischen kompressiblen und inkompressiblen Bereichen bestimmt das Abschirmverhalten. Randeffekte erweisen sich nur in solchen Magnetfeldintervallen als wichtig für die Abschirmung im Inneren einer streifenförmigen Probe, in denen (schon ohne aufgeprägte Modulation) in der Probenmitte ein neuer inkompressibler Streifen entsteht. Im Kapitel 4 wird die Rolle der inkompressiblen Streifen in einer idealisierten, streifenförmigen Hall-Probe untersucht. Mithilfe einer lokalen Version des Ohmschen Gesetzes berechnen wir bei vorgegebenen Gesamtstrom die Stromdichte und das nun ortsabhängige elektrochemische Potential, dessen Gradient die Stromdichte treibt. Für den lokalen Leitfähigkeitstensor nehmen wir ein für homogenes 2DES berechnetes Resultat und ersetzen den Füllfaktor jeweils durch den lokalen Wert. Dadurch ergibt sich, dass bei Existenz inkompressibler Streifen der gesamte Strom auf diese Streifen eingeschränkt ist, in denen die Komponenten des spezifischen Widerstands die Werte des freien, idealen 2DES haben, also verschwindenden longitudinalen und quantisierten Hall-Widerstand. Aus Hartree-Rechnungen zeigen wir, dass es inkompressible Streifen nur in Magnetfeldintervallen endlicher Breite (um ganzzahlige Füllfaktoren) gibt und dass in der Nähe von Füllfaktor 4 es nur inkompressible Streifen mit dem lokalen Füll-faktor \nu(x) = 4 gibt, aber nicht solche mit \nu(x) = 2, in Gegensatz zu dem Ergebnis der Thomas-Fermi-Poisson-Näherung, die hier nicht gültig ist. Um diese Unzulänglichkeit der Thomas-Fermi-Poisson-Näherung und Artefakte des strikt lokalen Modells zu beheben, führen wir die Rechnungen mit einem (auf der Skala des mittleren Elektronenabstands) gemittelten Leitfähigkeitstensors aus. Damit erhalten wir, im Rahmen einer Linear-Response-Rechnung, sehr schöne Übereinstimmung mit den Potentialmessungen, die diese Dissertation motivierten, einen kausalen Zusammenhang zwischen der Existenz inkompressibler Streifen und der Existenz von Plateaus im QHE, und ein Verständnis der extremen Genauigkeit, mit der die quantisierten Widerstandswerte reproduziert werden können, unabhängig von Probenmaterial und -geometrie. Im Kapitel 5 untersuchen wir das Zufallspotential, in dem sich die Elektronen bewegen. Wir gehen davon aus, dass sich hinter einer undotierten Schicht eine Ebene mit zufällig verteilten ionisierten Donatoren befindet, deren Coulomb-Potentiale sich zu dem Zufallspotential überlagern. Wir weisen darauf hin, dass sich die langreichweitigen Fluktuationen dieses Potentials anders verhalten als die kurzreichweitigen. Die kurzreichweitigen klingen mit dem Abstand der Donatorebene von der Ebene des 2DES exponentiell ab, werden aber (bei B = 0) nur schwach durch das 2DES abgeschirmt. Diese Fluktuationen haben wir durch die endlichen Leitfähigkeiten und die Stoßverbreiterung der Landau-Niveaus berücksichtigt. Die langreichweitigen Fluktuationen, andererseits, sind nur schwach von der Entfernung der Donatorebene abhängig, werden aber stark vom 2DES abgeschirmt. Diese sollte man bei der selbstkonsistenten Abschirmungsrechnung explizit berücksichtigen. Erste Versuche in dieser Richtung zeigen, dass sie die Quanten-Hall-Plateaus verbreitern, verschieben und stabilisieren können. Sie sollten besonders bei breiten Proben wichtig werden, bei denen sie zusätzliche inkompressible Streifen im Probeninneren verursachen können. Schließlich diskutieren wir in Kapitel 6 Abschirmungseffekte in einem Doppelschichtsystem aus zwei parallelen 2DES. Interessante neue Effekte treten auf, wenn die Schichten verschiedene Dichten haben. Das Auftreten inkompressibler Streifen in der einen Schicht kann dann drastische Auswirkungen auf die andere Schicht haben. Widerstandsmessungen in Abhängigkeit vom Magnetfeld, die kürzlich an solchen Systemen durchgeführt wurden, zeigen, dass am Rande eines QH-Plateaus Hysterese auftritt, d.h. dass die für ansteigendes Magnetfeld gemessene Kurve nicht mit der für abfallendes Magnetfeld gemessenen Kurve übereinstimmt, wenn dieser Magnetfeldbereich in ein QH-Plateau der anderen Schicht fällt. Wir entwickeln ein Modell und beschreiben Modellrechnungen, die dieses Phänomen plausibel machen.
In this PhD thesis, we develop models for the numerical simulation of epitaxial crystal growth, as realized, e.g., in molecular beam epitaxy (MBE). The basic idea is to use a discrete lattice gas representation of the crystal structure, and to apply kinetic Monte Carlo (KMC) simulations for the description of the growth dynamics. The main advantage of the KMC approach is the possibility to account for atomistic details and at the same time cover MBE relevant time scales in the simulation. In chapter 1, we describe the principles of MBE, pointing out relevant physical processes and the influence of experimental control parameters. We discuss various methods used in the theoretical description of epitaxial growth. Subsequently, the underlying concepts of the KMC method and the lattice gas approach are presented. Important aspects concerning the design of a lattice gas model are considered, e.g. the solid-on-solid approximation or the choice of an appropriate lattice topology. A key element of any KMC simulation is the selection of allowed events and the evaluation of Arrhenius rates for thermally activated processes. We discuss simplifying schemes that are used to approximate the corresponding energy barriers if detailed knowledge about the barriers is not available. Finally, the efficient implementation of the MC kinetics using a rejection-free algorithm is described. In chapter 2, we present a solid-on-solid lattice gas model which aims at the description of II-VI(001) semiconductor surfaces like CdTe(001). The model accounts for the zincblende structure and the relevant surface reconstructions of Cd- and Te-terminated surfaces. Particles at the surface interact via anisotropic nearest and next nearest neighbor interactions, whereas interactions in the bulk are isotropic. The anisotropic surface interactions reflect known properties of CdTe(001) like the small energy difference between the c(2x2) and (2x1) vacancy structures of Cd-terminated surfaces. A key element of the model is the presence of additional Te atoms in a weakly bound Te* state, which is motivated by experimental observations of Te coverages exceeding one monolayer at low temperatures and high Te fluxes. The true mechanism of binding excess Te to the surface is still unclear. Here, we use a mean-field approach assuming a Te* reservoir with limited occupation. In chapter 3, we perform KMC simulations of atomic layer epitaxy (ALE) of CdTe(001). We study the self-regulation of the ALE growth rate and demonstrate how the interplay of the Te* reservoir occupation with the surface kinetics results in two different regimes: at high temperatures the growth rate is limited to one half layer of CdTe per ALE cycle, whereas at low enough temperatures each cycle adds a complete layer. The temperature where the transition between the two regimes occurs depends mainly on the particle fluxes. The temperature dependence of the growth rate and the flux dependence of the transition temperature are in good qualitative agreement with experimental results. Comparing the macroscopic activation energy for Te* desorption in our model with experimental values we find semiquantitative agreement. In chapter 4, we study the formation of nanostructures with alternating stripes during submonolayer heteroepitaxy of two different adsorbate species on a given substrate. We evaluate the influence of two mechanisms: kinetic segregation due to chemically induced diffusion barriers, and strain relaxation by alternating arrangement of the adsorbate species. KMC simulations of a simple cubic lattice gas with weak inter-species binding energy show that kinetic effects are sufficient to account for stripe formation during growth. The dependence of the stripe width on control parameters is investigated. We find an Arrhenius temperature dependence, in agreement with experimental investigations of phase separation in binary or ternary material systems. Canonical MC simulations show that the observed stripes are not stable under equilibrium conditions: the adsorbate species separate into very large domains. Off-lattice simulations which account for the lattice misfit of the involved particle species show that, under equilibrium conditions, the competition between binding and strain energy results in regular stripe patterns with a well-defined width depending on both misfit and binding energies. In KMC simulations, the stripe-formation and the experimentally reported ramification of adsorbate islands are reproduced. To clarify the origin of the island ramification, we investigate an enhanced lattice gas model whose parameters are fitted to match characteristic off-lattice diffusion barriers. The simulation results show that a satisfactory explanation of experimental observations within the lattice gas framework requires a detailed incorporation of long-range elastic interactions. In the appendix we discuss supplementary topics related to the lattice gas simulations in chapter 4.
This thesis contains two major parts: The first part introduces the reader into three independent concepts of treating strongly correlated many body physics. These are, on the analytical side the SO(5)-theory (Chap.3), which poses the general frame. On the numerical side these are the Stochastic Series Expansion (SSE) (Chap.1) and the Contractor Renormalization Group (CORE) approach (Chap. 2}). The central idea of this thesis was to combine these above concepts, in order to achieve a better understanding of the high-T_c superconductors (HTSC). The results obtained by this combination can be found in the second major part of this thesis (chapters 4 and 5). The main idea of this thesis, i.e., to combine the SO(5)-theory with the capabilities of bosonic Quantum-Monte Carlo simulations and those of the CORE approach, has been proven to be a very successful Ansatz. Two different approaches, one based on symmetry and one on renormalization-group arguments, motivate an effective bosonic Hamiltonian. In a subsequent step the effective Hamiltonian has been simulated efficiently using the SSE. The results reproduce salient experiments on high-T_c superconductors. In addition, it has been shown that the model can be extended to capture also charge ordering. These results also form a profound basis for further studies, for example one could address the open question of SO(5)-symmetry restoration at a multicritical point in the extended pSO(5) model, where longer ranged interactions are included.
In this thesis we analyze CP violating effects of MSSM phases in production and two-body decays of neutralinos, charginos and sfermions. For different supersymmetric processes we define and calculate CP-odd asymmetries, which base on triple products. We present numerical results for electron-positron collisions at a future linear collider with a center of mass energy of 500-800 GeV, high luminosity and longitudinally polarized beams.
In this work, we studied in great detail how the unknown parameters of the SUSY seesaw model can be determined from measurements of observables at or below collider energies, namely rare flavor violating decays of leptons, slepton pair production processes at linear colliders and slepton mass differences. This is a challenging task as there is an intricate dependence of the observables on the unknown seesaw, light neutrino and mSUGRA parameters. In order to separate these different influences, we first considered two classes of seesaw models, namely quasi-degenerate and strongly hierarchical right-handed neutrinos. As a generalisation, we presented a method that can be used to reconstruct the high energy seesaw parameters, among them the heavy right-handed neutrino masses, from low energy observables alone.
This thesis aims at a description of the equilibrium dynamics of quantum spin glass systems. To this end a generic fermionic SU(2), spin 1/2 spin glass model with infinite-range interactions is defined in the first part. The model is treated in the framework of imaginary-time Grassmann field theory along with the replica formalism. A dynamical two-step decoupling procedure, which retains the full time dependence of the (replica-symmetric) saddle point, is presented. As a main result, a set of highly coupled self-consistency equations for the spin-spin correlations can be formulated. Beyond the so-called spin-static approximation two complementary systematic approximation schemes are developed in order to render the occurring integration problem feasible. One of these methods restricts the quantum-spin dynamics to a manageable number of bosonic Matsubara frequencies. A sequence of improved approximants to some quantity can be obtained by gradually extending the set of employed discrete frequencies. Extrapolation of such a sequence yields an estimate of the full dynamical solution. The other method is based on a perturbative expansion of the self-consistency equations in terms of the dynamical correlations. In the second part these techniques are applied to the isotropic Heisenberg spin glass both on the Fock space (HSGF) and, exploiting the Popov-Fedotov trick, on the spin space (HSGS). The critical temperatures of the paramagnet to spin glass phase transitions are determined accurately. Compared to the spin-static results, the dynamics causes slight increases of T_c by about 3% and 2%, respectively. For the HSGS the specific heat C(T) is investigated in the paramagnetic phase and, by way of a perturbative method, below but close to T_c. The exact C(T)-curve is shown to exhibit a pronounced non-analyticity at T_c and, contradictory to recent reports by other authors, there is no indication of maximum above T_c. In the last part of this thesis the spin glass model is augmented with a nearest-neighbor hopping term on an infinite-dimensional cubic lattice. An extended self-consistency structure can be derived by combining the decoupling procedure with the dynamical CPA method. For the itinerant Ising spin glass numerous solutions within the spin-static approximation are presented both at finite and zero temperature. Systematic dynamical corrections to the spin-static phase diagram in the plane of temperature and hopping strength are calculated, and the location of the quantum critical point is determined.
We investigate the single particle static and dynamic properties at zero temperature within the Hubbard an three-band-Hubbard model for the superconducting copper oxides. Based on the recently proposed self-energy functional approach (SFA) [M.Potthoff, Eur. Phys. J. B 32 429 (2003)], we present an extension of the cluster-perturbation theory (CPT) to systems with spontaneous broken symmetry. Our method accounts for both short-range correlations and long-range order. Short-range correlations are accurately taken into account via the exact diagonalization of finite clusters. Long-range order is described by variational optimization of a ficticious symmetry-breaking field. In comparison with related cluster methods, our approach is more flexible and, for a given cluster size, less demanding numerically, especially at zero temperature. An application of the method to the antiferromagnetic phase of the Hubbard model at half-filling shows good agreement with results from quantum Monte-Carlo calculations. We demonstrate that the variational extension of the cluster-perturbation theory is crucial to reproduce salient features of the single-particle spectrum of the insulating cuprates. Comparison of the dispersion of the low-energy excitations with recent experimental results of angular resolved photoemission spectroscopy (ARPES) allows us to fix a consistent parameter set for the one-band Hubbard model with an additional hopping parameter t' along the lattice diagonal. The doping dependence of the single-particle excitations is studied within the t-t-U Hubbard model with special emphasis on the electron doped compounds. We show, that the ARPES results on the band structure and the Fermi surface of Nd{2-x}Ce_xCuOCl_{4-\delta} are naturally obtained within the t-t-U Hubbard model without further need for readjustment or fitting of parameters, as proposed in recent theoretical considerations. We present a theory for the photon energy and polarization dependence of ARPES intensities from the CuO2 plane in the framework of strong correlation models. The importance of surface states for the observed experimental facts is considered. We show that for electric field vector in the CuO_2 plane the ‘radiation characteristics’ of the O 2p_{\sigma} and Cu 3d_{x^2-y^2} orbitals are strongly peaked along the CuO_2 plane, i.e. most photoelectrons are emitted at grazing angles. This suggests that surface states play an important role in the observed ARPES spectra, consistent with recent data from Sr_2CuCl_2O_2. We show that a combination of surface state dispersion and Fano resonance between surface state and the continuum of LEED-states may produce a precipitous drop in the observed photoelectron current as a function of in-plane momentum, which may well mimic a Fermi-surface crossing. This effect may explain the simultaneous ‘observation’ of a hole-like and an electron-like Fermi surfaces in Bi_2Sr_2CaCu_2O_{8+\delta} at different photon energies.
In this thesis, a phenomenological phase-fluctuation model for the pseudogap regime of the underdoped cuprates was discussed. The key idea of the phase-fluctuation scenario in the high-T_c superconductors is the notion that the pseudogap observed in a wide variety of experiments arises from phase fluctuations of the superconducting gap. In this scenario, below a mean-field temperature scale T_c^{MF}, a d_{x^2-y^2}-wave gap amplitude is assumed to develop. However, the superconducting transition is suppressed to a considerably lower transition temperature T_c by phase fluctuations. In the intermediate temperature regime between T_c^{MF} and T_c, phase fluctuations of the superconducting order parameter give rise to the pseudogap phenomena. The phenomenological phase-fluctuation model discussed in this thesis consists of a two-dimensional BCS-like Hamiltonian where the phase of the pairing-amplitude is free to fluctuate. The fluctuations of the phase were treated by a Monte Carlo simulation of a classical XY model. First, the density of states was calculated. The quasiparticle tunneling conductance (dI/dV) obtained from our phenomenological phase fluctuation model was able to reproduce characteristic and salient features of recent scanning-tunneling studies of Bi2212 and Bi2201 suggesting that the pseudogap behavior observed in these experiments arises from phase fluctuations of the d_{x^2-y^2}-wave pairing gap. In calculating the single-particle spectral weight, we were further able to show how phase fluctuations influence the experimentally observed quasiparticle spectra in detail. In particular the disappearance of the BCS-Bogoliubov quasiparticle band at T_c and the change from a more V-like superconducting gap to a rather U-like pseudogap above T_c can be explained in a consistent way by assuming that the low-energy pseudogap in the underdoped cuprates is due to phase fluctuations of a local d_{x^2-y^2}-wave pairing gap with fixed magnitude. Furthermore, phase fluctuations can explain why the pseudogap starts closing from the nodal points, whereas it rather fills in along the anti-nodal directions and they can also account for the characteristic temperature dependence of the superconducting (pi,0)-photoemission-peak. Next, we have shown that the "violation" of the low-frequency optical sum rule recently observed in the SC state of underdoped Bi2212, which is associated with a reduction of kinetic energy, can be related to the role of phase fluctuations. The decrease in kinetic energy is due to the sharpening of the quasiparticle peaks close to the superconducting transition at T_c == T_{KT}, where the phase correlation length xi diverges. A detailed analysis of the temperature and frequency dependence of the optical conductivity sigma(omega)=sigma_1(omega)+i sigma_2(omega) revealed a superconducting scaling of sigma_2(omega), which starts already above T_c, exactly as observed in high-frequency microwave conductivity experiments on Bi2212. On the other hand, our model was only able to account for the characteristic peak, which is observed in sigma_1(omega) close to the superconducting transition, after the inclusion of an additional marginal-Fermi-liquid scattering-rate in the optical conductivity formula. Finally, we calculated the static uniform diamagnetic susceptibility. It turned out that the precursor effects of the fluctuating diamagnetism above T_c are very small and limited to temperatures close to T_c in a phase-fluctuation scenario of the pseudogap. Instead, the temperature dependence of the uniform static magnetic susceptibility is dominated by the Pauli spin susceptibility, which displayed a very characteristic temperature dependence, independent of the details of the gap function used in our model. This temperature dependence is qualitatively very similar to the experimentally observed change of the Knight-shift as a function of temperature in underdoped Bi2212.
The four-dimensional Minkowski space is known to be a good description for space-time down to the length scales probed by the latest high-energy experiments. Nevertheless, there is the viable and exciting possibility that additional space-time structure will be observable in the next generation of collider experiments. Hence, we discuss different extensions of the standard model of particle physics with an extra dimension at the TeV-scale. We assume that some of the gauge and Higgs bosons propagate in one additional spatial dimension, while matter fields are confined to a four-dimensional subspace, the usual Minkowski space. After compactification on an S^1/Z_2 orbifold, an effective four-dimensional theory is obtained where towers of Kaluza-Klein (KK) modes, in addition to the standard model fields, reflect the higher-dimensional structure of space-time. The models are elaborated from the 5D Lagrangian to the Feynman rules of the KK modes. Special attention is paid to an appropriate generalization of the Rxi-gauge and the interplay between spontaneous symmetry breaking and compactification. Confronting the observables in 5D standard model extensions with combined precision measurements at the Z-boson pole and the latest data from LEP2, we constrain the possible size R of the extra dimension experimentally. A multi-parameter fit of all relevant input parameters leads to bounds for the compactification scale M=1/R in the range 4-6 TeV at the 2 sigma confidence level and shows how the mass of the Higgs boson is correlated with the size of an extra dimension. Considering a future linear e+e- collider, we outline the discovery potential for an extra dimension using the proposed TESLA specifications as an example. As a consistency check for the various models, we analyze Ward identities and the gauge boson equivalence theorem in W-pair production and find that gauge symmetry is preserved by a complex interplay of the Kaluza-Klein modes. In this context, we point out the close analogy between the traditional Higgs mechanism and mass generation for gauge bosons via compactification. Beyond the tree-level, the higher-dimensional models studied extensively in the literature and in the first part of this thesis have to be extended. We modify the models by the inclusion of brane kinetic terms which are required as counter terms. Again, we derive the corresponding 4D theory for the KK towers paying special attention to gauge fixing and spontaneous symmetry breaking. Finally, the phenomenological implications of the new brane kinetic terms are investigated in detail.
The Galactic Starburst Region NGC 3603 : exciting new insights on the formation of high mass stars
(2004)
One of the most fundamental, yet still unsolved problems in star formation research is addressed by the question "How do high mass stars form?". While most details related to the formation and early evolution of low mass stars are quite well understood today, the basic processes leading to the formation of high mass stars still remain a mystery. There is no doubt that low mass stars like our Sun form via accretion of gas and dust from their natal environment. With respect to the formation of high mass stars theorists currently discuss two possible scenarios controversely: First, similar to stars of lower masses, high mass stars form by continuous (time variable) accretion of large amounts of gas and dust through their circumstellar envelopes and/or disks. Second, high mass stars form by repeated collisions (coalescence) of protostars of lower masses. Both scenarios bear difficulties which impose strong constrains on the final mass of the young star. To find evidences for or against one of these two theoretical models is a challenging task for observers. First, sites of high mass star formation are much more distant than the nearby sites of low mass star formation. Second, high mass stars form and evolve much faster than low mass star. In particular, they contract to main sequence, hydrogen burning temperatures and densities on time scales which are much shorter than typical accretion time scales. Third, as a consequence of the previous point, young high mass stars are usually deeply embedded in their natal environment throughout their (short) pre-main sequence phase. Therefore, high mass protostars are rare, difficult to find and difficult to study. In my thesis I undertake a novel approach to search for and to characterize high mass protostars, by looking into a region where young high mass stars form in the violent neighbourhood of a cluster of early type main sequence stars. The presence of already evolved O type stars provides a wealth of energetic photons and powerful stellar winds which evaporate and disperse the surrounding interstellar medium, thus "lifting the courtains" around nearby young stars at a relatively early evolutionary stage. Such premises are given in the Galactic starburst region NGC 3603. Nevertheless, a large observational effort with different telescopes and instruments -- in particular, taking advantage of the high angular resolution and high sensitivity of near and mid IR instruments available at ESO -- was necessary to achieve the goals of my study. After a basic introduction on the topic of (high mass) star formation in Chapter 1, a short overview of the investigated region NGC 3603 and its importance for both galactic and extragalactic star formation studies is given in Chapter 2. Then, in Chapter 3, I report on a comprehensive investigation of the distribution and kinematics of the molecular gas and dust associated with the NGC 3603 region. In Chapter 4 I thoroughly address the radial extent of the NGC 3603 OB cluster and the spatial distribution of the cluster members. Together with deep Ks band imaging data, a detailed survey of NGC 3603 at mid IR wavelengths allows to search the neighbourhood of the cold molecular gas and dust for sources with intrinsic mid IR excess (Chapter 5). In Chapter 6 I characterize the most prominent sources of NGC 3603 IRS 9 and show that these sources are bona-fide candidates for high mass protostars. Finally, a concise summary as well as an outlook on future prospects in high mass star formation research is given in Chapter 7.
In this work the supersymmetric seesaw model and its effects on low-energy leptonic observables and thermal leptogenesis have been systematically investigated. Precision measurements will increase the sensitivity on lepton-flavor violating decays, particularly on Br(l_j->l_i gamma) and also on electric and magnetic dipole moments in the near future. In order to improve also the accuracy of theoretical predictions for these processes, we have performed a full one-loop calculation of the underlying supersymmetric processes taking into account the lepton masses. Since the mechanism of soft supersymmetry breaking (SSB) is completely unknown, a novel analysis beyond the often studied minimal Supergravity scenarios has been performed. This way it has been demonstrated that in the considered mSUGRA, AMSB, GMSB and gaugino mediated scenarios, the ongoing search for Br(mu->e gamma) can constrain fundamental SSB parameters and/or the seesaw parameters. On the other hand, the basic parameters of thermal leptogenesis, such as the CP asymmetry in the decays of the lightest right-handed Majorana neutrino, provide probes of the unknown complex orthogonal R-matrix of the seesaw model.