Using quantum equations of motion for interacting bosons, stochastic molecular dynamics simulations with quantized momenta are performed for Lennard-Jones helium-4. The viscosity of the quantum liquid is significantly less than that of the classical liquid, being almost 5 times smaller at the lowest temperature studied. The classical and quantum liquids are identical except for Bose-Einstein condensation, which pinpoints the molecular mechanism for superfluidity. The results rely on the existence of stochastic but real particle trajectories, which has implications for the interpretation of quantum mechanics.
Using quantum equations of motion for interacting bosons, stochastic molecular dynamics simulations with quantized momenta are performed for Lennard-Jones helium-4. The viscosity of the quantum liquid is significantly less than that of the classical liquid, being almost 5 times smaller at the lowest temperature studied. The classical and quantum liquids are identical except for Bose-Einstein condensation, which pinpoints the molecular mechanism for superfluidity. The results rely on the existence of stochastic but real particle trajectories, which has implications for the interpretation of quantum mechanics.
Decoherent quantum equations of motion are derived that yield the trajectory of an open quantum system. The viscosity of superfluid Lennard-Jones helium-4 is obtained with a quantum stochastic molecular dynamics algorithm. The momentum state occupancy entropy is counted with a continuous representation of boson number and averages are obtained with umbrella sampling. Instantaneous snapshots of the Bose-Einstein condensed system show multiple highly occupied momentum states. The viscosity is obtained from the Onsager-Green-Kubo relation with the time correlation function modified in the quantum case. On the saturation curve, at higher temperatures the viscosities of the classical and quantum liquids are equal. With decreasing temperature the viscosity of the classical liquid increases whereas that of the quantum liquid decreases. Below the λ-transition the viscosity lies significantly below the classical value, being small but positive due to the mixture of condensed and uncondensed bosons. The computed trajectories give a physical explanation of the molecular mechanism for superfluidity.
The two-fluid theory for superfluidity is not entirely consistent with the evidence for condensation into multiple highly occupied momentum states. On the far side of the -transition wave function symmetrisation is in the form of pure momentum loops and momentum state occupancy, the non-local nature of which gives inviscid plug flow, and the entropy of which gives the superfluid critical velocity. Equations of motion for condensed bosons conserve entropy. A quantum stochastic molecular dynamics algorithm based on a continuous form of occupancy gives the viscosity of liquid 4He, which is less than the classical calculation, increasingly so as the temperature is decreased through the condensation transition. Molecular trajectories show the suppression of collisions that transfer longitudinal momentum laterally in the superfluid regime. A second algorithm that treats condensed bosons in the same momentum state as a rigid body with non-local forces also yields a reduced viscosity but with greater uncertainty.
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
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.
The goal of this chapter will be to briefly describe the remarkable properties of helium at low temperatures. After stating some of these properties we will see how they can be understood in terms of the phenomenon of Bose–Einstein condensation described in Chapter 7. We will give the main argument in two different formulations, once using the quasi-particle method of Bogoliubov, and then using a Green function approach. We start with some experimental facts. Helium is a remarkable element. It was predicted to exist from observations of the Sun before it was found on Earth. It is the only element which remains a liquid at zero temperature and atmospheric pressure. Experimentally the phase diagram of 4 He is shown in Figure 10.1. Helium I is a normal fluid and has a normal gas-liquid critical point. Helium II is a mixture of a normal fluid and a superfluid. The superfluid is characterized by the vanishing of its viscosity. Helium I and helium II are separated by a line known as the λ -transition line. At T λ = 2.18 K, P λ = 2.29 Pa, helium I, helium II, and helium gas coexist. The specific heat of liquid helium along the vapor transition line forms a logarithmic discontinuity shown in Figure 10.2. The form of this diagram resembles the Greek letter λ and is the reason for calling the transition a λ -transition. The lack of viscosity of helium II leads to some remarkable experimental consequences, one of which we briefly describe. Let two containers A and B be linked by a thin capillary through which only a fluid with zero (or very low) viscosity can pass freely.
The quantum mechanics of a system of identical interacting particles must lead to the classical hydrodynamic equations of motion at high temperatures, because of the correspondence principle. On the other hand, the behaviour of helium II shows that this is not always the case at low temperatures. In this paper it is shown that in certain cases the quantum description requires an extra parameter, which is the potential of a new velocity field superimposed on the classical motion. Expressed in semi-classical terms, the condition for the existence of this new parameter is that the probability, in the equilibrium state, of a particle having a very large de Broglie wavelength (that is, a negligible momentum) is finite. This condition is satisfied in one model of a superfluid system, a condensed Bose-Einstein gas, but not in a crystal. A tentative theoretical interpretation of two basic equations of the empirical two-fluid theory of helium II is given, in which this new parameter determines the velocity of the superfluid.