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Soviet Journal of Low Temperature Physics

Hydrodynamics of a superfluid in the weak interaction model

Н. М. Лавріненко, S. V. Peletminskiǐ, Yu. V. Slyusarenko

Published Aug 1, 1983• 1 citation
Publisher

Abstract

The equations of the hydrodynamics of a superfluid with υk – uk≠0 (υk and uk are the velocities of the superfluid and normal components) are derived with allowance made for dissipative processes. It is shown that in this case the system is described by 14 kinetic coefficients. The low-temperature asymptotic forms of all these coefficients for the υk− uk≠0 case are considered.

DOI
10.1063/10.0030960

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The equations of the hydrodynamics of a superfluid with υk – uk≠0 (υk and uk are the velocities of the superfluid and normal components) are derived with allowance made for dissipative processes. It is shown that in this case the system is described by 14 kinetic coefficients. The low-temperature asymptotic forms of all these coefficients for the υk− uk≠0 case are considered.
This review presents a microscopic construction of the thermodynamics and hydrodynamics of superfluid bosons and fermions with singlet pairing, based on the concept of quasiaverages and the hypothesis of reduced description. Here we do not assume that the Hamiltonian possesses any dynamical symmetry. This has permitted obtaining results pertaining to both Galilean-invariant and relativistic systems. Account is taken of dissipative processes. The kinetic coefficients are presented in terms of the correlation functions of the flux operators. The approach is extended to solutions of quantum liquids. The influence of an external ac field on superfluid systems is studied, and the low-frequency asymptotic behavior of the Green's function is found in the hydrodynamic approximation. The symmetry properties of the equilibrium state are formulated, and the thermodynamics is constructed for superfluid Fermi systems with triplet pairing (the superfluid phases 3 He-B and 3 He-A). For the latter the flux densities of the additive integrals of motion are found in a state of equilibrium and the equations of "ideal" hydrodynamics are derived.
Based on an assumption of the existence of an inner and gauge symmetry between two superfluid components, a phenomenological derivation of equations of relativistic superfluidity theory for systems with two types of condensates is given in a non-dissipative approximation. The effect of mutual dragging of superfluid components is considered as a consequence of interaction of condensates treated as quantum scalar fields. Thermodynamics identities for the pressure, energy and expression for the energy-momentum tensor are found. The limit of low velocities is considered.
A system of hydrodynamic equations has been obtained for superfluid Fermi systems with singlet pairing and nonzero momentum which are formed, e.g., in the case of small polarization of the spin system. As a result, the energy gap is a periodic function of the coordinates and a spin-density wave is formed. For such systems the complete set of dynamic variables includes both purely hydrodynamic (superfluid and normal) velocities and the displacement vector corresponding to the violations of the translational invariance. All of the tensors of normal and superfluid densities that appear in the system as well as the elastic moduli have been calculated. A dispersion relation has been obtained for thermal vibrations (second sound) and elastic vibrations, and this relation has turned out to be substantially anisotropic. Observation of the predicted effects is most probable in 3He–He II solutions in magnetic fields of the order of several kilooersteds at low temperatures.
It is shown that three-velocity hydrodynamics equations describing the properties of a two-condensate crystal determine the low-frequency spectrum with allowance for superfluid drag. The drag on one superfluid component of density ρ12(s) from another component of density ρ22(s), gives rise to two branches of vibrations of frequencies ω1 and ω2, unlike the case of a one-condensate crystal. The absorption coefficient for transverse sound in a one-condensate crystal is expressed in terms of the quantum-mechanical characteristic quantity that describes the tunneling of atoms.
Abstract Chapter 2 describes the basic knowledge of Bose-condensed systems in order to study the quantum hydrodynamics for both the superfluid helium and the atomic-gas BECs in the following sections. Starting from the field theoretical formulation, we will first give a self-contained explanation of the derivation of the most fundamental GP equation for weakly interacting Bose gases at zero temperature. We will also highlight the theoretical treatment for incorporating the concept of elementary excitations to describe low-energy excitations of Bose systems, the definition of normal and superfluid components, and eventually the celebrated model of two-fluid hydrodynamics. Finally, the microscopic structure and dynamics of topological excitations obtained from the GP equation are discussed by exemplifying solitons, vortex lines, and vortex rings.
Abstract In this paper, we develop an appropriate set of hydrodynamic equations for a U(N) invariant superfluid that couple the dynamics of superflow and magnetization. In the special case when both the superfluid and normal velocities are zero, the hydrodynamic equations reduce to a generalized version of Landau–Lifshitz equation for ferromagnetism with U(N) symmetry. When both velocities are non-zero, there appears couplings between the superflow and magnetization dynamics, and the superfluid velocity no longer satisfies the irrotational condition. On the other hand, the magnitude of magnetization is no longer a constant of motion as was the case for the standard Landau–Lifshitz theory. In comparison with the simple superfluid, the first and second sounds are modified by a non-zero magnetization through various thermodynamic functions. For U(2) invariant superfluid, we get both (zero-) sound wave and a spin wave at zero temperature. It is found that the dispersion of spin wave is always quadratic, which is consistent with microscopic analysis. In the appendix, we show that the hydrodynamic equation for a U(N) invariant superfluid can be obtained from the general hydrodynamic equation with arbitrary internal symmetries.