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We develop a joint formalism and numerical framework for analyzing the superconducting instability of metals from a weak coupling perspective. This encompasses the Kohn–Luttinger formulation of weak coupling renormalization group for superconductivity as well as the random phase approximation imposed on the diagrammatic expansion of the two-particle Green’s function. The central quantity to resolve is the effective interaction in the Cooper channel, for which we develop an optimized numerical framework. Our code is capable of treating generic multi-orbital models in two as well as three spatial dimensions and, in particular, arbitrary avenues of spin-orbit coupling.
We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with the goal of finding an optimized scheme. Using the square lattice t-t' Hubbard model as a testbed we define and benchmark the quality. Most notably we define an error estimate of the solution for the ordinary differential equation circumventing the issues introduced by the divergences at the end of the FRG flow. Using this measure to control for accuracy we find a threefold reduction in number of required integration steps achievable by choice of integrator. We herewith publish a set of recommended choices for the functional renormalization group, shown to decrease the computational cost for FRG calculations and representing a valuable basis for further investigations.
A well-known result for the interference of two single-mode fields is that the degree of coherence and the degree of indistinguishability are the same when we consider the detection of a single photon. In this article, we present the relation between the degree of coherence, path indistinguishability and the fringe visibility considering interference of multiple numbers of single-mode fields while being interested in the detection of a single photon only. We will also mention how Born’s rule of interference for multiple sources is reflected in these results.
In response to the 2013 Update of the European Strategy for Particle Physics, the Future Circular Collider (FCC) study was launched, as an international collaboration hosted by CERN. This study covers a highest-luminosity high-energy lepton collider (FCC-ee) and an energy-frontier hadron collider (FCC-hh), which could, successively, be installed in the same 100 km tunnel. The scientific capabilities of the integrated FCC programme would serve the worldwide community throughout the 21st century. The FCC study also investigates an LHC energy upgrade, using FCC-hh technology. This document constitutes the second volume of the FCC Conceptual Design Report, devoted to the electron-positron collider FCC-ee. After summarizing the physics discovery opportunities, it presents the accelerator design, performance reach, a staged operation scenario, the underlying technologies, civil engineering, technical infrastructure, and an implementation plan. FCC-ee can be built with today's technology. Most of the FCC-ee infrastructure could be reused for FCC-hh. Combining concepts from past and present lepton colliders and adding a few novel elements, the FCC-ee design promises outstandingly high luminosity. This will make the FCC-ee a unique precision instrument to study the heaviest known particles (Z, W and H bosons and the top quark), offering great direct and indirect sensitivity to new physics.
Cardiovascular disease is one of the leading causes of death worldwide and, so far, echocardiography, nuclear cardiology, and catheterization are the gold standard techniques used for its detection. Cardiac magnetic resonance (CMR) can replace the invasive imaging modalities and provide a "one-stop shop" characterization of the cardiovascular system by measuring myocardial tissue structure, function and perfusion of the heart, as well as anatomy of and flow in the coronary arteries. In contrast to standard clinical magnetic resonance imaging (MRI) scanners, which are often operated at a field strength of 1.5 or 3 Tesla (T), a higher resolution and subsequent cardiac parameter quantification could potentially be achieved at ultra-high field, i.e., 7 T and above.
Unique insights into the pathophysiology of the heart are expected from ultra-high field MRI, which offers enhanced image quality in combination with novel contrast mechanisms, but suffers from spatio-temporal B0 magnetic field variations. Due to the resulting spatial misregistration and intra-voxel dephasing, these B0-field inhomogeneities generate a variety of undesired image artifacts, e.g., artificial image deformation. The resulting macroscopic field gradients lead to signal loss, because the effective transverse relaxation time T2* is shortened. This affects the accuracy of T2* measurements, which are essential for myocardial tissue characterization. When steady state free precession-based pulse sequences are employed for image acquisition, certain off-resonance frequencies cause signal voids. These banding artifacts complicate the proper marking of the myocardium and, subsequently, systematic errors in cardiac function measurements are inevitable. Clinical MR scanners are equipped with basic shim systems to correct for occurring B0-field inhomogeneities and resulting image artifacts, however, these are not sufficient for the advanced measurement techniques employed for ultra-high field MRI of the heart.
Therefore, this work focused on the development of advanced B0 shimming strategies for CMR imaging applications to correct the spatio-temporal B0 field variations present in the human heart at 7 T. A novel cardiac phase-specific shimming (CPSS) technique was set up, which featured a triggered B0 map acquisition, anatomy-matched selection of the shim-region-of-interest (SROI), and calibration-based B0 field modeling. The influence of technical limitations on the overall spherical harmonics (SH) shim was analyzed. Moreover, benefits as well as pitfalls of dynamic shimming were debated in this study. An advanced B0 shimming strategy was set up and applied in vivo, which was the first implementation of a heart-specific shimming approach in human UHF MRI at the time.
The spatial B0-field patterns which were measured in the heart throughout this study contained localized spots of strong inhomogeneities. They fluctuated over the cardiac cycle in both size and strength, and were ideally addressed using anatomy-matched SROIs. Creating a correcting magnetic field with one shim coil, however, generated eddy currents in the surrounding conducting structures and a resulting additional, unintended magnetic field. Taking these shim-to-shim interactions into account via calibration, it was demonstrated for the first time that the non-standard 3rd-order SH terms enhanced B0-field homogeneity in the human heart. However, they were attended by challenges for the shim system hardware employed in the presented work, which was indicated by the currents required to generate the optimal 3rd-order SH terms exceeding the dynamic range of the corresponding shim coils. To facilitate dynamic shimming updated over the cardiac cycle for cine imaging, the benefit of adjusting the oscillating CPSS currents was found to be vital. The first in vivo application of the novel advanced B0 shimming strategy mostly matched the simulations.
The presented technical developments are a basic requirement to quantitative and functional CMR imaging of the human heart at 7 T. They pave the way for numerous clinical studies about cardiac diseases, and continuative research on dedicated cardiac B0 shimming, e.g., adapted passive shimming and multi-coil technologies.
We review the physics opportunities of the Future Circular Collider, covering its e(+)e(-), pp, ep and heavy ion programmes. We describe the measurement capabilities of each FCC component, addressing the study of electroweak, Higgs and strong interactions, the top quark and flavour, as well as phenomena beyond the Standard Model. We highlight the synergy and complementarity of the different colliders, which will contribute to a uniquely coherent and ambitious research programme, providing an unmatchable combination of precision and sensitivity to new physics.
In response to the 2013 Update of the European Strategy for Particle Physics (EPPSU), the Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. The FCC study covered an energy-frontier hadron collider (FCC-hh), a highest-luminosity high-energy lepton collider (FCC-ee), the corresponding 100 km tunnel infrastructure, as well as the physics opportunities of these two colliders, and a high-energy LHC, based on FCC-hh technology. This document constitutes the third volume of the FCC Conceptual Design Report, devoted to the hadron collider FCC-hh. It summarizes the FCC-hh physics discovery opportunities, presents the FCC-hh accelerator design, performance reach, and staged operation plan, discusses the underlying technologies, the civil engineering and technical infrastructure, and also sketches a possible implementation. Combining ingredients from the Large Hadron Collider (LHC), the high-luminosity LHC upgrade and adding novel technologies and approaches, the FCC-hh design aims at significantly extending the energy frontier to 100 TeV. Its unprecedented centre-of-mass collision energy will make the FCC-hh a unique instrument to explore physics beyond the Standard Model, offering great direct sensitivity to new physics and discoveries.
In response to the 2013 Update of the European Strategy for Particle Physics (EPPSU), the Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. The FCC study covered an energy-frontier hadron collider (FCC-hh), a highest-luminosity high-energy lepton collider (FCC-ee), the corresponding 100km tunnel infrastructure, as well as the physics opportunities of these two colliders, and a high-energy LHC, based on FCC-hh technology. This document constitutes the third volume of the FCC Conceptual Design Report, devoted to the hadron collider FCC-hh. It summarizes the FCC-hh physics discovery opportunities, presents the FCC-hh accelerator design, performance reach, and staged operation plan, discusses the underlying technologies, the civil engineering and technical infrastructure, and also sketches a possible implementation. Combining ingredients from the Large Hadron Collider (LHC), the high-luminosity LHC upgrade and adding novel technologies and approaches, the FCC-hh design aims at significantly extending the energy frontier to 100TeV. Its unprecedented centre of-mass collision energy will make the FCC-hh a unique instrument to explore physics beyond the Standard Model, offering great direct sensitivity to new physics and discoveries.
Narrow resonances decaying into WW, WZ or ZZ boson pairs are searched for in 139 fb(-1) of proton-proton collision data at a centre-of-mass energy of root s = 13TeV recorded with the ATLAS detector at the Large Hadron Collider from 2015 to 2018. The diboson system is reconstructed using pairs of high transverse momentum, large-radius jets. These jets are built from a combination of calorimeter- and tracker-inputs compatible with the hadronic decay of a boosted W or Z boson, using jet mass and substructure properties. The search is performed for diboson resonances with masses greater than 1.3TeV. No significant deviations from the background expectations are observed. Exclusion limits at the 95% confidence level are set on the production cross-section times branching ratio into dibosons for resonances in a range of theories beyond the Standard Model, with the highest excluded mass of a new gauge boson at 3.8TeV in the context of mass-degenerate resonances that couple predominantly to gauge bosons.
Josephson junctions (JJs) in the presence of a magnetic field exhibit qualitatively different interference patterns depending on the spatial distribution of the supercurrent through the junction. In JJs based on two-dimensional topological insulators (2DTIs), the electrons/holes forming a Cooper pair (CP) can either propagate along the same edge or be split into the two edges. The former leads to a SQUID-like interference pattern, with the superconducting flux quantum ϕ\(_0\) (where ϕ\(_0\)=h/2e) as a fundamental period. If CPs’ splitting is additionally included, the resultant periodicity doubles. Since the edge states are typically considered to be strongly localized, the critical current does not decay as a function of the magnetic field. The present paper goes beyond this approach and inspects a topological JJ in the tunneling regime featuring extended edge states. It is here considered the possibility that the two electrons of a CP propagate and explore the junction independently over length scales comparable to the superconducting coherence length. As a consequence of the spatial extension, a decaying pattern with different possible periods is obtained. In particular, it is shown that, if crossed Andreev reflections (CARs) are dominant and the edge states overlap, the resulting interference pattern features oscillations whose periodicity approaches 2ϕ\(_0\).