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CLASSIFICATION OF SPATIALLY-NONUNIFORM EQUILIBRIUM STATES OF SUPERFLUIDS

Mikhail Yurievich Kovalevsky, Наталья Николаевна Чеканова

Published Jan 1, 2001• 0 citations
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Abstract

The classification of equilibrium states of superfluid with scalar, vector and tensor order parameters is carried out on the basis of the quasiaveragues concept. The generalization of a requirement of the residual symmetry for nonuniform equilibrium states is given. The admissible requirements of a spatial symmetry in the terms of integrals of motion are found. The connection of these requirements with helicoidal structure of vectors of a spin and spatial anisotropy is established. At some restrictions is shown, that the equilibrium structure of an order parameter can be represented as product of a nonuniform part, depending on spatial coordinates, and homogeneous part of an order parameter.

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The classification of equilibrium states of superfluid with scalar, vector and tensor order parameters is carried out on the basis of the quasiaveragues concept. The generalization of a requirement of the residual symmetry for nonuniform equilibrium states is given. The admissible requirements of a spatial symmetry in the terms of integrals of motion are found. The connection of these requirements with helicoidal structure of vectors of a spin and spatial anisotropy is established. At some restrictions is shown, that the equilibrium structure of an order parameter can be represented as product of a nonuniform part, depending on spatial coordinates, and homogeneous part of an order parameter.
A classification of the equilibrium states of a quantum liquid with d pairing is given on the basis of the concept of quasi-averages. The order-parameter operator is represented in terms of Fermi operators. It is shown that the set of such equilibrium states can be classified in terms of the quantum number corresponding to the projection of the orbital angular momentum of a Cooper pair on the anisotropy direction. The explicit form of the three admissible generators of the unbroken symmetry is found and the corresponding equilibrium values of the order parameter are obtained. A generalization to possible nonuniform equilibrium structures is carried out, and the corresponding form of the order parameter of such structures is found.
The problem of classification of degenerate equilibrium states in spin s = 1 systems with the phase and magnetic symmetries simultaneously broken is considered. An assumption about the residual symmetry of degenerate equilibrium states and the transformation properties of the spinor order-parameter operator under transformations generated by additive integrals of motion yields equations that classify its equilibrium values. The anisotropic structure of the equilibrium values of the order parameter is presented in terms of the parameters of the residual symmetry generator. Based on the model with a separated condensate, the structure of the densities of the magnetic additive integrals of motion in the equilibrium state is revealed. A comparison is made with the results of existing studies on superfluid spin s = 1 systems.
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 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.
A discussion of an anisotropic (ppp state) Fermi superfluid with a spatially varying order parameter is presented. We restrict ourself to the Landau-Ginzburg region and consider spatial variations governed by the linear gap equation. The kernel of the linearized gap equation is shown to be related to a current-current correlation function of quasiparticles in the normal state. This relation permits the calculation of the two coherence lengths ${\ensuremath{\xi}}_{L}$ and ${\ensuremath{\xi}}_{T}$ defined earlier in the framework of a phenomenological Landau-Ginzburg theory, and a discussion of boundary conditions for the order parameter at interfaces. A significant anisotropy in the coherence lengths is found (${\ensuremath{\xi}}_{L}=\sqrt{3}{\ensuremath{\xi}}_{T}$), which reflects itself in the nature of the supercurrents. The boundary conditions at specularly and diffusely reflecting surfaces lead us to expect that the vector $\stackrel{^}{l}$, which describes the orbital angular momentum of a Cooper pair in an "axial" state, is anchored normal to the walls. Some consequences of these results on various experimental problems (fourth sound, monodomain production, Josephson couplings, behavior in thin capillaries) are briefly discussed.
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.