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Cooper pairing of fermions is a profound phenomenon that has become very important in many different areas of physics in the recent past. This book brings together, for the first time, experts from various fields involving Cooper pairing, at the level of BCS theory and beyond, including the study of novel states of matter such as ultracold atomic gases, nuclear systems at the extreme, and quark matter with application to neutron stars. Cross-disciplinary in nature, the book will be of interest to physicists in many different specialties, including condensed matter, nuclear, high-energy, and a

Fermions. --- Many-body problem. --- Pairing correlations (Nuclear physics) --- Superconductivity. --- Correlations, Pairing (Nuclear physics) --- Hartree-Fock approximation --- Wave functions --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Mechanics, Analytic --- Electric conductivity --- Critical currents --- Superfluidity --- Fermi-Dirac particles --- Particles (Nuclear physics) --- Quantum statistics --- Interacting boson-fermion models --- Leptons (Nuclear physics)

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A new science emerges at the intersection of modern physics, computer s- ence,andmaterialscience. Thestruggletofurtherminiaturizeisputtingna- technology to the verge of creating single-electron and/or single-spin devices that operate by moving a single electron (spin) and can serve as transistors, memory cells, and for logic gates. These devices take advantage of quantum physics that dominates nanometer size scales. The devices that utilize met- based hybrid nanostructures may possess signi?cant advantages over those exploiting purely semiconducting materials. First, the chemistry of metals is typically simpler than that of semiconductors. Second, the electric properties of metals are much less sensitive to the structural defects and impurities than those of semiconductors. Next, metallic devices allow better electric and th- mal contacts. Another important plus point is that in metals the electron de Broigle wavelength is smaller by many orders of magnitude as compared to that in semiconductors. This makes metallic devices more promising with respect to their size - down to the size of an atom. Further, high bulk and interface thermal conductance in metallic devices are bene?cial for the heat withdraw. And, last but by no means the least, the high electron velocity in metals promises to accelerate enormously operation rates with respect to those in semiconductor-based devices. The ?nal note is that metals can - hibit strong ferromagnetism and/or superconductivity.

Quantum theory --- Transport theory --- Nanostructured materials --- Physics. --- Quantum physics. --- Condensed matter. --- Superconductivity. --- Superconductors. --- Magnetism. --- Magnetic materials. --- Quantum computers. --- Spintronics. --- Quantum Physics. --- Condensed Matter Physics. --- Strongly Correlated Systems, Superconductivity. --- Magnetism, Magnetic Materials. --- Quantum Information Technology, Spintronics. --- Magnetoelectronics --- Spin electronics --- Microelectronics --- Nanotechnology --- Computers --- Materials --- Mathematical physics --- Physics --- Electricity --- Magnetics --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Electronics --- Solid state electronics --- Electric conductivity --- Critical currents --- Superfluidity --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Quantum theory. --- Fluxtronics --- Spinelectronics --- Quantum transport --- Metallic nanostructures --- Hybrid nanostructures --- NATO

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Since the first experimental achievement of Bose–Einstein condensates (BEC) in 1995 and the award of the Nobel Prize for Physics in 2001, the properties of these gaseous quantum fluids have been the focus of international interest in physics. This monograph is dedicated to the mathematical modelling of some specific experiments which display vortices and to a rigorous analysis of features emerging experimentally. In contrast to a classical fluid, a quantum fluid such as a Bose–Einstein condensate can rotate only through the nucleation of quantized vortices beyond some critical velocity. There are two interesting regimes: one close to the critical velocity, where there is only one vortex that has a very special shape; and another one at high rotation values, for which a dense lattice is observed. One of the key features related to superfluidity is the existence of these vortices. We address this issue mathematically and derive information on their shape, number, and location. In the dilute limit of these experiments, the condensate is well described by a mean field theory and a macroscopic wave function solving the so-called Gross–Pitaevskii equation. The mathematical tools employed are energy estimates, Gamma convergence, and homogenization techniques. We prove existence of solutions that have properties consistent with the experimental observations. Open problems related to recent experiments are presented. The work can serve as a reference for mathematical researchers and theoretical physicists interested in superfluidity and quantum fluids, and can also complement a graduate seminar in elliptic PDEs or modelling of physical experiments.

Quantum mechanics. Quantumfield theory --- Solid state physics --- Bose-Einstein condensation. --- Vortex-motion. --- Lattice dynamics. --- Dynamics, Lattice --- Crystal lattices --- Phonons --- Solids --- Aerodynamics --- Eddies --- Fluid dynamics --- Hydrodynamics --- Rotational motion --- Bose condensed fluids --- Bose condensed liquids --- Bose fluids --- Bose liquids --- Einstein condensation --- Bosons --- Condensation --- Superfluidity --- Differential equations, partial. --- Mathematical physics. --- Mathematics. --- Partial Differential Equations. --- Strongly Correlated Systems, Superconductivity. --- Mathematical Methods in Physics. --- Condensed Matter Physics. --- Classical and Continuum Physics. --- Applications of Mathematics. --- Math --- Science --- Physical mathematics --- Physics --- Partial differential equations --- Mathematics --- Partial differential equations. --- Superconductivity. --- Superconductors. --- Physics. --- Condensed matter. --- Continuum physics. --- Applied mathematics. --- Engineering mathematics. --- Classical field theory --- Continuum physics --- Continuum mechanics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Electronics --- Solid state electronics --- Electric conductivity --- Critical currents --- Engineering --- Engineering analysis --- Mathematical analysis --- Materials

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2 Homogeneous superconducting state 210 3 Superconducting phases with broken space symmetries 213 4 Flavor asymmetric quark condensates 219 5 Concluding remarks 221 Acknowledgments 222 References 223 Neutral Dense Quark Matter 225 Mei Huang and Igor Shovkovy 1 Introduction 225 2 Local charge neutrality: homogeneous phase 226 3 Global charge neutrality: mixed phase 234 4 Conclusion 238 References 238 Possibility of color magnetic superconductivity 241 Toshitaka Tatsumi, Tomoyuki Maruyama, and Eiji Nakano 1 Introduction 241 2 What is ferromagnetism in quark matter? 243 3 Color magnetic superconductivity 248 4 Chiral symmetry and magnetism 253 5 Summary and Concluding remarks 258 Acknowledgments 260 References 260 Magnetic Fields of Compact Stars with Superconducting Quark Cores 263 David M. Sedrakian, David Blaschke, and Karen M. Shahabasyan 1 Introduction 263 2 Free Energy 265 3 Ginzburg-Landau equations 267 4 Vortex Structure 269 5 Solution of Ginzburg-Landau Equations 271 6 The Magnetic Field Components 273 7 Summary 275 Acknowledgments 275 References 275 Thermal Color-superconducting Fluctuations in Dense Quark Matter 277 D. N.

Astronomie --- Astronomy --- Sterrenkunde --- Quantum chromodynamics. --- Stars --- Big bang theory. --- Chromodynamique quantique --- Etoiles --- Big bang --- Constitution. --- Constitution --- Quantum chromodynamics --- Compact objects (Astronomy) --- Big bang theory --- Nuclear Physics --- Astrophysics --- Physics --- Astronomy & Astrophysics --- Physical Sciences & Mathematics --- Compact EPUB-LIV-FT LIVPHYSI QCD SPRINGER-B matter stars --- Big bang cosmology --- Superdense theory --- Chromodynamics, Quantum --- QCD (Nuclear physics) --- Physics. --- Gravitation. --- Astrophysics. --- Nuclear physics. --- Heavy ions. --- Hadrons. --- Elementary particles (Physics). --- Quantum field theory. --- Superconductivity. --- Superconductors. --- Astrophysics and Astroparticles. --- Elementary Particles, Quantum Field Theory. --- Nuclear Physics, Heavy Ions, Hadrons. --- Classical and Quantum Gravitation, Relativity Theory. --- Strongly Correlated Systems, Superconductivity. --- Cosmogony --- Cosmology --- Expanding universe --- Astronomical spectroscopy --- Particles (Nuclear physics) --- Quantum electrodynamics --- Congresses --- Formation --- Quantum theory. --- Atomic nuclei --- Atoms, Nuclei of --- Nucleus of the atom --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Electronics --- Solid state electronics --- Electric conductivity --- Critical currents --- Superfluidity --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Ions --- Relativistic quantum field theory --- Quantum theory --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Astronomical physics --- Cosmic physics --- Materials --- Properties --- Compact stars --- QCD matter