The modern theory of Bose-Einstein condensation, superfluidity, and superconductivity is reviewed. The thermodynamic principle for superfluid flow and the equation of motion for condensed bosons are given. Computer simulations of Lennard-Jones $^4$He give the $λ$-transition and the superfluid viscosity. The statistical mechanical theory of high-temperature superconductivity is presented. Critical comparison is made with older approaches, such as ground energy state condensation, irrotational superfluid flow, and the macroscopic wavefunction.
The modern theory of Bose-Einstein condensation, superfluidity, and superconductivity is reviewed. The thermodynamic principle for superfluid flow and the equation of motion for condensed bosons are given. Computer simulations of Lennard-Jones 4He give the λ-transition and the superfluid viscosity. The statistical mechanical theory of high-temperature superconductivity is presented. Critical comparison is made with older approaches, such as ground energy state condensation, irrotational superfluid flow, and the macroscopic wavefunction.
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
Bose-Einstein condensation and the λ-transition are described in molecular detail for bosons interacting with a pair potential. New phenomena are identified that are absent in the usual ideal gas treatment. Monte Carlo simulations of Lennard-Jones helium-4 neglecting ground momentum state bosons give a diverging heat capacity approaching the transition. Pure permutation loops give continuous growth in the occupancy of the ground momentum state. Mixed ground and excited momentum state permutation loops give a discontinuous transition to the condensed phase. The consequent latent heat for the λ-transition is 3\% of the total energy. The predicted critical velocity for superfluid flow is within a factor of three of the measured values over three orders of magnitude in pore diameter.
The study of exotic states of matter, particularly superfluids and Bose-Einstein condensates (BECs), has revolutionized our understanding of quantum mechanics in macroscopic systems. This article explores the thermodynamic properties of these states, focusing on their unique behavior at ultra-low temperatures. Superfluids exhibit zero viscosity and anomalous flow characteristics, while Bose-Einstein condensates, formed by cooling bosons to near absolute zero, present quantum phenomena on a macroscopic scale. This paper reviews key thermodynamic concepts, such as entropy, heat capacity, and chemical potential, as they apply to these exotic phases. Additionally, the relationship between quantum coherence and thermodynamic stability in superfluids and BECs is examined, along with the practical implications for quantum technologies.
This paper represents the full version of a paper published earlier in Physica A [246 (1997), 275]. The present paper includes argumentation, proofs and details omitted in the shortened version. The papers are a further development of the approach in quantum statistical mechanics proposed by the author. The hierarchy of equations for reduced density matrices obtained previously is extended to the case corresponding to the Bose-Einstein condensation. The relevant state of the system with a condensate can be superfluid as well as nonsuperfluid. Special attention is given to the thermodynamics of superfluid systems. According to the results of the papers superfluidity is the state of a fluid whose symmetry is spontaneously broken because of a stationary flow. The state corresponds to thermodynamic equilibrium while the magnitude of the flow depends upon the temperature and is determined by thermodynamic considerations. The equations obtained are solved in two simple cases. The physical origin of superfluidity, peculiarities of the phenomenon in closed volumes and the critical velocity are discussed as well.
This chapter introduces the basic physics of Bose--Einstein condensation. We first start with why there is a difference between distinguishable and indistinguishable particles in terms of the number of states that are available in a composite system. Then Bose and Einstein's argument of why one expects a high probability of occupation of the ground state is discussed. This is derived then more rigorously for the grand canonical ensemble, showing that at some critical temperature there should be a macroscopic occupation of the ground state. Next, the low-lying energy spectrum of an interacting Bose--Einstein condensate is derived, leading to the Bogoliubov dispersion. The significance of the Bogoliubov dispersion as the origin of superfluidity is then discussed, in terms of superfluditysuperfluidity. Laudau'sLandau's criterion for superfluidity is derived, by general principles of Galilean transformations of Schrodinger's equation.
The main objective of this paper is to introduce a new quantum mechanism of condensates and superconductivity based on a new interpretation of quantum mechanical wavefunctions, and on recent developments in quantum physics and statistical physics. First, we postulate that the wavefunction [Formula: see text]e[Formula: see text] is the common wavefunction for all particles in the same class determined by the external potential V(x), [Formula: see text](x)[Formula: see text] represents the distribution density of the particles, and [Formula: see text] is the velocity field of the particles. Although the new interpretation does not alter the basic theories of quantum mechanics, it is an entirely different interpretation from the classical Bohr interpretation, removes all absurdities and offers new insights for quantum physics and for condensed matter physics. Second, we show that the key for condensation of bosonic particles is that their interaction is sufficiently weak to ensure that a large collection of boson particles are in a state governed by the same condensation wavefunction field [Formula: see text] under the same bounding potential V. For superconductivity, the formation of superconductivity comes down to conditions for the formation of electron pairs, and for the electron pairs to share a common wavefunction. Thanks to the recently developed principle of interaction dynamics (PID) interaction potential of electrons and the average-energy level formula of temperature, these conditions for superconductivity are explicitly derived. Furthermore, we obtain both microscopic and macroscopic formulas for the critical temperature. The field and topological phase transition equations for condensates are also derived.