Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Soviet Physics Uspekhi

On the microscopic theory of superfluid liquids

N. N. Bogolyubov, M. Yu. Kovalevskiĭ, A. M. Kurbatov, S. V. Peletminskiǐ, A. N. Tarasov

Published Dec 31, 1989• 24 citations
Publisher

Abstract

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.

DOI
10.1070/pu1989v032n12abeh002782

Related papers

Quasiaverages in microscopic theory of quantum liquids

A. A. Isayev, Mikhail Yurievich Kovalevsky

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.

Journal of Physical Studies•Jan 1, 1997•1 citation

Symmetry of Equilibrium State and Hydrodynamics Equation of a Superfluid Fermi-liquid

Mikhail Yurievich Kovalevsky, Alexander Alimovich Rozhkov

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.

Telecommunications and Radio Engineering•Jan 1, 2001•0 citations

Theory of a superfluid Fermi liquid

Alexander I. Akhiezer, Красильников Владимир Владимирович, S. V. Peletminskiǐ +1 more

A Fermi-liquid approach to the theory of superfluidity is developed, based on a generalization of the combinatoric expression for the entropy to the case in which the state of the Fermi liquid is described not only by a normal but also by an anomalous distribution function. The energy of the superfluid Fermi liquid is given in the form of a functional of these distribution functions. In the weak-coupling approximation the Fermi-liquid approach is equivalent to the BCS theory. The interaction between the Fermi liquid and an electromagnetic field is gauge invariant. In addition to the singlet-pairing theory the triplet-pairing theory is also developed. A unified variational principle that gives rise to the theory of superfluidity (superconductivity) is used to obtain the London equations and the Ginzburg–Landau equation. Applications of this theory are made to the derivation of an equation for ideal two-component hydrodynamics.

Physics-Uspekhi•Feb 28, 1993•13 citations

Thermo- and hydrodynamics of the B-phase of a superfluid Fermi liquid

M. Yu. Kovalevskiĭ, Александр Алимович Рожков

Hydro- and thermodynamics of the B-phase of a superfluid Fermi liquid are described using the Fermi-liquid approach. The spectra of natural oscillations of the system are obtained and analyzed. The Cartan form and the superfluid momentum are expressed in terms of the order parameters. An expression connecting the fluxes of physical quantities in the local equilibrium state is derived. The hydro- and thermodynamic equations are presented in the Galilean and relativistic forms.

Low Temperature Physics•Nov 1, 1995•2 citations

Microscopic derivation of the hydrodynamic equations for the superfluid fermi-systems

Pavlo Shygorin, Svidzynsky

Starting from the first principles of statistical mechanics, the two-fluid hydrodynamics of superconductor in ideal approximation is constructed.The system of equations of motion for normal and anomalous correlation functions is used for hydrodynamic description.Transition to equations of hydrodynamics is performed using an expansion of equations of motion for correlation functions in terms of a small parameter.

Condensed Matter Physics•Jan 1, 2005•0 citations

Hydrodynamics and proper vibrations of quantum liquids with conformational degrees of freedom

Mikhail Yurievich Kovalevsky, A. A. Rozhkov

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.

The Journal of V N Karazin Kharkiv National University Series Physics•Jan 1, 2020•0 citations
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.
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.
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.
A Fermi-liquid approach to the theory of superfluidity is developed, based on a generalization of the combinatoric expression for the entropy to the case in which the state of the Fermi liquid is described not only by a normal but also by an anomalous distribution function. The energy of the superfluid Fermi liquid is given in the form of a functional of these distribution functions. In the weak-coupling approximation the Fermi-liquid approach is equivalent to the BCS theory. The interaction between the Fermi liquid and an electromagnetic field is gauge invariant. In addition to the singlet-pairing theory the triplet-pairing theory is also developed. A unified variational principle that gives rise to the theory of superfluidity (superconductivity) is used to obtain the London equations and the Ginzburg–Landau equation. Applications of this theory are made to the derivation of an equation for ideal two-component hydrodynamics.
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.