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CRC Press eBooks

Molecular Dynamics of Superfluidity

Phil Attard

Published Oct 25, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1201/9781003506416-5

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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.
The ninth chapter analyses interacting bosons on the far side of the λ-transition, showing that the partition function factorizes into the classical configuration integral and ideal non-local pure momentum permutation loops. Results include: condensation is into multiple multiply-occupied momentum states, the permutation loop entropy suppresses collisions, inviscid plug flow results from non-locality, and the predicted superfluid critical velocity quantitatively agrees with measured values. The fountain pressure between chambers of different temperature is quantitatively accounted for by the minimization of energy at constant subsystem entropy, which principle is a direct consequence of dissipationless superfluid flow. Superfluid equations of motion explain how collisions occur without dissipating the momentum of the condensed bosons.
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 λλλ-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.
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.
Bose-Einstein condensation at low temperatures is driven by occupation entropy, since configurations of labeled particles with multiply-occupied states have more weight. An open quantum system collapses into decoherent states weighted by the reservoir entropy. Thus arises quantum statistical mechanics in classical phase space. The symmetrization function generalizes quantum state occupancy to the momentum continuum. Hamilton's classical equations of motion hold only for an open quantum system with negligible condensation. In the condensed regime the molecular equations of motion preserve the entropy, consistent with fountain pressure measurements of superfluid flow. Condensed bosons in the same momentum state experience non-local forces and move as a rigid body that does not dissipate momentum in classical collisions. High-temperature superconductivity is statistical mechanical in nature, requires bound fermion pairs of neighboring electrons, and is driven by the monotonic-oscillatory transition at high charge coupling.
Actually, the fundamental feature of Bose condensation is the macroscopic occupation of a single quantum state, whatever that state may be. As long as such a macroscopically-occupied state exists, the system will exhibit superfluid behavior. Superfluid flow thus appears as a "collective" phenomenon, in which the particles move together in order to preserve the macroscopic occupation of a single state. The equilibrium is metastable, because obviously there exists a state of lower energy, that of the fluid at rest; the essential point is that no transitions to the latter state will take place. Metastable superfluid flow is only possible because it involves condensate motion. The superfluid velocity is thus proportional to the gradient of the phase of the condensate wave-function. The superfluid motion is thus a uniform translation, in contrast with ordinary viscous flow, for which the fluid velocity varies from the walls to the center of the tube.
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 4^44He give the λλλ-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.