Abstract This chapter starts with a discussion of the symmetry conditions which have to be imposed on the wave function of a many-particle system, and the distinction between bosons and fermions. It then examines the consequences of these conditions for simple systems of non-interacting particles (Fermi-Dirac and Bose-Einstein statistics), and in particular, introduces the phenomenon of Bose-Einstein condensation (BEC) in a noninteracting Bose gas. The phenomenon of Cooper pairing of interacting fermions is introduced by a thought-experiment in which one starts from a BEC of tightly bound diatomic molecules made of fermion atoms and gradually weakens the binding. The chapter closes with a description of the various physical systems to be treated in the book, and an account of the phenomenology of superfluidity and superconductivity. An appendix treats the statistical mechanics of a rotating system.
Abstract This chapter starts with a discussion of the symmetry conditions which have to be imposed on the wave function of a many-particle system, and the distinction between bosons and fermions. It then examines the consequences of these conditions for simple systems of non-interacting particles (Fermi-Dirac and Bose-Einstein statistics), and in particular, introduces the phenomenon of Bose-Einstein condensation (BEC) in a noninteracting Bose gas. The phenomenon of Cooper pairing of interacting fermions is introduced by a thought-experiment in which one starts from a BEC of tightly bound diatomic molecules made of fermion atoms and gradually weakens the binding. The chapter closes with a description of the various physical systems to be treated in the book, and an account of the phenomenology of superfluidity and superconductivity. An appendix treats the statistical mechanics of a rotating system.
Abstract Starting from first principles, this book introduces the closely related phenomena of Bose condensation and Cooper pairing, in which a very large number of single particles or pairs of particles are forced to behave in exactly the same way. Their consequences in condensed matter systems are also explored. Eschewing advanced formal methods, the book uses simple concepts and arguments to account for the various qualitatively new phenomena which occur in Bose-condensed and Cooper-paired systems, including but not limited to the spectacular macroscopic phenomena of superconductivity and superfluidity. The physical systems discussed include liquid 4-He, the BEC alkali gases, “classical” superconductors, superfluid 3-He, “exotic” superconductors, and the recently stabilized Fermi alkali gases.
Abstract The book covers three main strands, Bose-Einstein condensates (BEC), superfluid and superconductivity. The subjects are developed in a way which gradually builds up the key concepts and the necessary mathematical machinery. The book begins with the simplest of the three topics, BEC, and first thoroughly reviews the basics of the Bose-Einstein ideal gas before going into the techniques of magnetic trapping and cooling of atoms and the discovery of BEC in dilute atomic gases. Superfluidity in helium-4 is more difficult to understand, because it is a strongly interacting quantum liquid. The book introduces the main physical phenomena of superfluidity, and how it follows from the key concept of macroscopic quantum coherence and off-diagonal long ranged order. The theory of superconductivity is developed in stages, starting with the simpler London and Ginzburg Landau theories and their main applications, before developing the mathematical concepts of a quantum coherent state and the Bardeen Cooper Schrieffer (BCS) theory. The final chapter deals with the more advanced topics, including superfluid helium-3 and evidence for unconventional Cooper pairing in exotic superconductors. No prior knowledge of quantum many-body theory is assumed, and the necessary mathematical concepts are introduced in a self-contained manner where needed.
Starting from first principles, this book introduces the closely related phenomena of Bose condensation and Cooper pairing, in which a very large number of single particles or pairs of particles are forced to behave in exactly the same way, and explores their consequences in condensed matter systems. Eschewing advanced formal methods, the author uses simple concepts and arguments to account for the various qualitatively new phenomena which occur in Bose-condensed and Cooper-pairedsystems, including but not limited to the spectacular macroscopic phenomena of superconductivity and superfluidity.
Bose-Einstein condensation, superfluidity, and superconductivity are quantum mechanics made visible. They mark the boundary between the classical and the quantum worlds, and they show the macroscopic role of quantum mechanics in condensed matter. This book presents these phenomena in terms of particles, their positions, and their momenta, giving a concrete visualisation and description that is not possible with traditional wave functions. A single approach that bridges the classical-quantum divide provides new insight into the role of particle interactions in condensation, the nature of collisions in superfluid flow, and the physical form of Cooper pairs in high-temperature superconductors. High-temperature superconductivity is explored with quantum statistical mechanics, which links it to Bose-Einstein condensation. Identifying a new mechanism for Cooper pairing, this explains the differences between the low- and high-temperature superconducting regimes and the role of the molecular structure of the conductor. The new perspective offered by this book on Bose-Einstein condensation, superfluidity, and high-temperature superconductivity gives particle-based explanations as well as mathematical and computational methods for these macroscopic quantum phenomena so that readers understand the role of particle interactions and structure in the physics of these phenomena. This book will appeal to undergraduate and graduate students, lecturers, academics, and scientific researchers in the fields of Bose-Einstein condensation and condensates, superfluidity, and superconductivity. It will also be of interest to those working with thermodynamics, statistical mechanics, statistical physics, quantum mechanics, molecular dynamics, materials science, condensed matter physics, and theoretical chemistry. Key Features: · Explores Bose-Einstein condensation with new evidence for multiple condensed states and novel Monte Carlo simulations for interacting bosons · Establishes the thermodynamic nature of condensed bosons from an analysis of fountain pressure measurements, including that they carry energy and entropy, and the thermodynamic principle of superfluid flow · Derives equations of motion for condensed bosons, and performs molecular dynamics simulations of the viscosity with molecular trajectories that give rise to superfluidity · Identifies the mechanism for electron pairing in high-temperature superconductivity
As we all know, single microscopic particles such as electrons or atoms do not behave according to the familiar classical (Newtonian) physics which describes the everyday world, but rather according to the prescriptions of quantum mechanics, the outcome is often bizarre and counterintuitive. When a macroscopic number of such particles (say ∼ 10) is assembled under conditions where the effects of quantum mechanics are important, the results can be even more spectacular; they include macroscopic phenomena such as superfluidity and superconductivity, which are completely impossible to explain in classical terms. Most, though not all of these exotic phenomena, are a result of a phenomenon which I shall refer to generically as “quantum condensation,” in which a macroscopic number of particles or pairs of particles—a nonzero fraction of all particles present—occupy a single quantum state; this phenomenon is traditionally referred to as Bose-Einstein condensation (BEC) when it occurs in a system of bosons such as liquid He, and as Cooper pairing when it occurs, for pairs of particles, in a system of fermions such as the electrons in a superconducting metal. As a result of quantum condensation, the characteristically quantum-mechanical behavior which we are used to seeing at the level of single electrons is as it were amplified by the cooperation of condensed particles and can manifest itself at the macroscopic level. The present essay is intended as a general introduction to the subject of quantum condensation and its consequences, as manifested in a variety of physical systems. I will try to review the fundamental physical ideas, usually without de-
Abstract Chapter 11 presents a statistical mechanical treatment of the quantum ideal gases, i.e., the ideal Boltzmann, fermion, and boson gases. The discussion begins with the microscopic description and the solution of the eigenvalue problem for a quantum ideal gas. It is argued that calculating the partition function is most readily accomplished in the grand canonical ensemble using a second-quantized formulation. When the particles are distinguishable, the equation of state is identical to that of a classical ideal gas. For fermions and bosons, however, the problem of computing thermodynamic properties is significantly more complex and can only be solved exactly in certain limits. Away from these limits approximations are needed and are discussed in detail. The relevant distributions - the Fermi-Dirac and Bose-Einstein distributions are derived. The local density approximation of density functional theory is derived for the ideal electron gas. For the ideal boson gas, the phenomenon of Bose-Einstein condensation is discussed