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Journal of Physical Studies

Quasiaverages in microscopic theory of quantum liquids

A. A. Isayev, Mikhail Yurievich Kovalevsky

Published Jan 1, 1997• 1 citation
Publisher

Abstract

An approach based on the method of quasiaverages and the reduced description method is developed as a microscopic tool for the derivation of hydrodynamic equations for super uid liquids with triplet pairing of quasiparticles.Additional thermodynamic parameters connected with different spontaneously broken symmetries of the system are determined with the use of the order parameter operator as functionals of the nonequilibrium statistical operator.The ux densities of additive motion integrals are obtained in terms of the locally equilibrium thermodynamic potential.Selfconsistent equations for the energy gap and quasiparticle energy are found which are analyzed for the unitary and nonunitary states of super uid Fermi{liquid.

DOI
10.30970/jps.01.389

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An approach based on the method of quasiaverages and the reduced description method is developed as a microscopic tool for the derivation of hydrodynamic equations for super uid liquids with triplet pairing of quasiparticles.Additional thermodynamic parameters connected with different spontaneously broken symmetries of the system are determined with the use of the order parameter operator as functionals of the nonequilibrium statistical operator.The ux densities of additive motion integrals are obtained in terms of the locally equilibrium thermodynamic potential.Selfconsistent equations for the energy gap and quasiparticle energy are found which are analyzed for the unitary and nonunitary states of super uid Fermi{liquid.
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.
Three kinds of quantum liquids are considered. Order parameter operators are written for two quantum liquids (where spontaneous breaking of symmetry takes place), and its commutation properties are considered. Symmetry properties of the equilibrium state are noted and expressions of order parameters of operator means in the equilibrium state are obtained. Expressions of basic thermodynamical relations in terms of the local equilibrium of thermodynamical potential are obtained. Nondissipative hydrodynamics equations are derived for all three liquids. The relationship connecting the densities of fluxes of additive motion integrals is obtained in the local equilibrium state.
The Fermi-liquid approach generalized to superfluid systems is used to derive general formulas for the normal and abnormal distribution functions (DF) for quasiparticles of a superfluid Fermi liquid (SFL) consisting of electrically neutral fermions with spin-triplet pairing (the spin of a pair s=1, the orbital angular momentum l of the pair being an arbitrary odd number) in a static uniform magnetic field, taking into account the Landau spin-exchange Fermi-liquid interaction at temperatures 0<T<Tc (Tc is the temperature of phase transition from the normal to the superfluid state). In deriving the DF, the explicit form of the energy functional (EF) for SFL is not used. A system of coupled equations is obtained for the order parameter, energy of quasiparticles, and effective magnetic field for the SFL under investigation in the case of an EF quadratic in DF. The obtained DF and the system of equations are applicable for describing both unitary and nonunitary phases of superfluid He3 in a magnetic field, e.g., for determining the magnetization and magnetic susceptibility of these phases.
The order parameters are constructed for a Fermi liquid with conformational degrees of freedom. Based on them, additional thermodynamic parameters were introduced: the spin unit vector dα (determining the anisotropy in the spin subspace), the unit spatial vectors mi and ni (determining the anisotropy in space), and also three scalar parameters determining the shape of the Cooper pair u, v, q ( first two items are half-axes of ellipsoid of Cooper pair and last item is mutual orientation in space of these half axes). The symmetry properties of the order parameter operator are considered. The equations of ideal hydrodynamics of a Fermi liquid are derived taking into account the influence of conformational degrees of freedom. By conformational degrees of freedom should be understood the parameters associated with the shape and size of the Cooper pair. Expressions are obtained for the flows of thermodynamic quantities of such a Fermi liquid in terms of the density of the energy functional. The energy functional depends both on the additive integrals of motion (classical fluid parameters) and on conformational parameters. The dispersion equation of such a liquid is obtained for a model representation of the energy functional (the work was performed as part of the Fermi-liquid approach). The dispersion equation includes spin modes, first, second, and third sounds. The dispersion equation for the spatial subsystem, including the first, second, and third sounds characteristic of superfluid systems, is analyzed. Particular solutions of the dispersion equation are simulated using the Maple software package (several 3D figures are given for the angular dependence of the speeds of 1 and 2 sounds in a spherical coordinate system). All of the above allows us to conclude that such a Fermi liquid can be considered as a superfluid liquid crystal of a nematic type. The presence of conformational parameters distinguishes the considered phase from the F phase of a superfluid Fermi liquid.
In the present paper, we consider the theory, describing both spiral magnetics and superfluid Fermi-liquid with a triplet pairing. Previously this method was used in the description of a superfluid Fermi-liquid in the singlet case. This approach is a generalization of the classical theory of Fermi-liquid. This semiphenomenological study combines the advantages of both the microscopic and phenomenological description. The method permits the spectra of collective excitations of the system to be obtained taking into account the Fermi-liquid effects.