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

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

Pavlo Shygorin, Anatoliy V. Svidzynskyi, Павло Павлович Шигорін, А. В. Свидзинский

Published Jan 1, 2005• 0 citations
Publisher

Abstract

Starting from the first principles of statistical mechanics the two-fluid hydrodynamics of superconductor in ideal approximation is constructed. For construction of hydrodynamics the system of equation of motion for a normal and an anomalous correlation functions are used. The transition to equations of hydrodynamics is execute with help an expansion of equations of motion for correlation functions in terms of a small parameter. Виходячи з перших принципів статистичної механіки, побудовано дворідинну гідродинаміку надпровідника в ідеальному наближенні. Для побудови гідродинаміки використано систему рівнянь руху для нормальної та аномальної кореляційних функцій. Перехід до рівнянь гідродинаміки здійснюється через розклад рівнянь руху для кореляційних функцій за малим параметром.

DOI
10.5488/cmp.8.4.701

Related papers

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

Microscopic derivation of the hydrodynamic equations for the superfluid Fermi system: Application to the two-fluid hydrodynamic equations in superfluid 3He-B

Jun’ichiro Hara, Katsuhiko Nagai

Journal of Low Temperature Physics•Feb 1, 1979•9 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

Fundamentals of superfluid hydrodynamics in Bose-condensed systems

Tsubota Makoto, Kasamatsu Makoto

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.

•Dec 2, 2025•0 citations

On the microscopic theory of superfluid liquids

N. N. Bogolyubov, M. Yu. Kovalevskiĭ, A. M. Kurbatov +2 more

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.

Soviet Physics Uspekhi•Dec 31, 1989•24 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
Starting from the first principles of statistical mechanics the two-fluid hydrodynamics of superconductor in ideal approximation is constructed. For construction of hydrodynamics the system of equation of motion for a normal and an anomalous correlation functions are used. The transition to equations of hydrodynamics is execute with help an expansion of equations of motion for correlation functions in terms of a small parameter. Виходячи з перших принципів статистичної механіки, побудовано дворідинну гідродинаміку надпровідника в ідеальному наближенні. Для побудови гідродинаміки використано систему рівнянь руху для нормальної та аномальної кореляційних функцій. Перехід до рівнянь гідродинаміки здійснюється через розклад рівнянь руху для кореляційних функцій за малим параметром.
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.
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.
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.
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.