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 astrophysics. The emphasis is on novel issues beyond ordinary BCS theory such as pairing in asymmetric systems, the polarization effect, and higher spin pairing. These topics are rarely treated at the textbook level and all of them are the subjects of intensive ongoing research. The book also considers various new techniques widely used in current research that differ significantly from the conventional condensed matter approaches described in the standard literature. Sample Chapter(s). Chapter 1: Color Superconductivity in Dense, but not Asymptotically Dense, Quark Matter (1,976 KB). Contents: Color Superconductivity in Dense, But Not Asymptotically Dense, Quark Matter (M Alford & K Rajagopal); Larkin-Ovchinnikov-Fulde-Ferrell Phases in QCD (G Nardulli); Phase Diagram of Neutral Quark Matter at Moderate Densities (S B Rster et al.); Spontaneous Nambu-Goldstone Current Generation Driven by Mismatch (M Huang); The CFL Phase and m s: An Effective Field Theory Approach (T Schnfer); Nuclear Superconductivity in Compact Stars: BCS Theory and Beyond (A Sedrakian & J W Clark); Pairing Properties of Dressed Nucleons in Infinite Matter (W H Dickhoff & H Mther); Pairing in Higher Angular Momentum States: Spectrum of Solutions of the 3 P 2 - 3 F 2 Pairing Model (M V Zverev et al.); Four-Particle Condensates in Nuclear Systems (G RApke & P Schuck); Realization, Characterization, and Detection of Novel Superfluid Phases with Pairing Between Unbalanced Fermion Species (K Yang); Phase Transition in Unbalanced Fermion Superfluids (H Caldas). Readership: Researchers and graduate students in the areas of condensed matter, nuclear and particle physics."

At first glance, the articles in this book may appear to have nothing in common. They cover such seemingly disparate subjects as the properties of small metallic clusters and the behavior of superfluid He3, nuclear physics and organic materials, copper oxides and mag netic resonance. Why have they been brought together, particUlarly in our time of narrow spe cialization? In fact, the properties and effects described in this book touch upon one and the same fundamental phenomenon: pair correlation. Introduced in the theory of superconductivity by J. Bardeen, L. Cooper, and J. Schrieffer (BCS), this effect plays a key role in various Fermi systems. The book consists of several sections. The first chapter is concerned with conven tional and high Tc superconductors. The second chapter describes two relatively young fami lies of superconductors: organics and fullerenes. Chapter III addresses the superfluidity of 3 He • The discovery of this phenomenon in 1971 was a big event in physics and last year was acknowledged by a Nobel prize. This book contains the text of the Nobel lecture. Chapters IV and V are devoted to correlations in finite Fermi systems such as small metallic clusters, C 60 anions, and atomic nuclei. The book thus covers a broad range of problems, illuminating the close ties between various areas of physics.

This dissertation covers my theoretical work in the field of pairing of fermions and BCS-BEC crossover behavior in various condensed matter systems. High temperature superconductors, heavy fermion systems, 2D semiconductors undergoing a semiconductor-superconductor transition, and ultracold atomic Fermi gases are examples of novel systems that provide us with a rich playground to study pairing phenomena such as superconductivity or superfluidity. In this dissertation, with ultracold fermions in mind, I attempt to address some of the outstanding theoretical issues regarding pairing of fermions for arbitrary interactions, and for arbitrary population and mass imbalance. In so doing, I explore pairing in Bose-Einstein condensation EC) and Bardeen-Cooper-Schrieffer CS) regimes, and the behavior at the BEC-BCS crossover. I investigate the stability of paired many-fermion ground states, e.g., superfluidity and phase separated states; and possible phase transitions between these ground states. The specific projects that I undertake at the mean-field level are: interplay of intra- and inter- species pairing correlations in determining s-wave pairing in spin-population imbalanced Fermi systems; p-wave pairing in systems with mismatched fermi surfaces; stability of "breached pairs" states with p-wave symmetry in BEC and BCS regimes; use of Bogoliubov-de Gennes equations to study spatial variation of the pairing order parameter; and superconductivity with unconventional pairing symmetries in 2D systems with an "inherent" gaps, such as in semiconducting systems. In the case of s-wave pairing in a spin-population imbalanced system, while the system phase separates into normal and superfluid components, I show that the inclusion of intra-species correlation stabilizes a supefluid phase, up to a critical polarization, on the BCS side. For S=1, ms=0 triplet p-wave pairing in a population imbalanced system, I obtain a rich phase diagram. In addition to the states Δ"1 propto Y1"1, a multitude of "mixed" SF states formed of linear combinations of Y1m's give global energy minimum under a phase stability condition. States with local minimum are also obtained. With increased polarization, the global minimum SF states may undergo a quantum phase transition to the local minimum SF states. I also study effects of finite temperature (T) and of mass imbalance (r) between the species. Though the features of the phase diagram are not changed qualitatively from the equal mass (r=1) case, the critical temperature Tc shows some interesting behavior for large polarization. Our p-wave pairing provides an arena to study "breached pairing" P), i.e., phase separation in momentum space. While this is not stable in BCS regime for s-wave pairing, I find that p-wave BP phases may be stable in both BCS and BEC regimes for arbitrary mass ratio, r. To explore many-body effects beyond mean-field, I study the effects of quantum fluctuations on equilibrium and pairing properties in BEC and BCS regimes and near the crossover (unitarity limit). I apply this to systems subjected to p-wave Feshbach resonance and compare with the results for the s-wave case. I also study the effects of these fluctuations on possible suppression of the superfluid transition temperature from dilute to dense regimes and at unitarity, and find the suppression factor of 2.2 to be quite robust, except close to unitarity. Specific systems to which my work may apply are population imbalanced cold atomic systems, 2D systems with "inherent gap", such as semiconducting systems, and strongly correlated Fermi systems close to the unitarity limit at the BEC-BCS crossover. My research utilizes method of many-body quantum field theory, quantum statistical mechanics, diagrammatic perturbation theory, notions of superconductivity and superfluidity at and beyond mean-field level. In many instances, I have developed detailed and reliable computer codes relevant to my work.

This unique volume reviews more than fifty years of theoretical and experimental developments of the concept that properties of atomic nuclei up to a great extent are defined by the pair correlations of nuclear constituents — protons and neutrons. Such correlations in condensed matter are responsible for quantum phenomena on a macroscopic level — superfluidity and superconductivity. After introducing Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity of metals, it became clear that atomic nuclei have properties of superfluid drops, and practically all features of nuclei strongly depend on the pair correlations. Presenting a comprehensive overview of the progress of nuclear science, the contributions from leading physicists around the world, cover the whole spectrum of studies in nuclear physics and physics of other small systems. With the most updated information written in an accessible way, the volume will serve as an irreplaceable source of references covering many years of development and insight into several new problems at the frontiers of science. It will be useful not only for physicists working in nuclear and condensed matter physics, astrophysicists, chemists and historians of science, but will also help students understand the current status and perspectives for the future.

This series on condensed matter theories provides a forum for advanced theoretical research in quantum many-body theory. The contributions are highly interdisciplinary, emphasizing common concerns among theorists who apply many-particle methods in such diverse areas as solid-state, low-temperature, statistical, nuclear, particle, and biological physics, as well as in quantum field theory, quantum information and the theory of complex systems. Each individual contribution is preceded by an extended introduction to the topic treated. Useful details not normally presented in journal articles can be found in this volume. Sample Chapter(s). Part A: Fermi Liquids: Pressure Comparison Between the Spherical Cellular Model and the Thomas-Fermi Model (290 KB). Contents: Condensation of Helium in Wedges (E S Hernindez et al.); Pairing in Asymmetrical Fermi Systems (K F Quader & R Liao); Quantum Boltzmann Liquids (K A Gernoth et al.); Fractionally Charged Excitations on Frustrated Lattices (E Runge et al.); On the de HaasOCoVan Alphen Oscillation in 2D (S Fujita & D L Morabito); The Concept of Correlated Density and Its Application (K Morawetz et al.); Pairing of Strongly Correlated Nucleons (W H Dickhoff); KohnOCoSham Calculations Combined with an Average Pair-Density Functional Theory (P Gori-Giorgi & A Savin); Maxent Approach to Qubits (C M Sarris et al.); Ergodic Condition and Magnetic Models (M H Lee); and other papers. Readership: Physicists, chemists and applied mathematicians interested in advanced theories of condensed matter and their applications."