Relativistic Kinetics of Phonon Gas in Superfluids

TL;DR

This paper develops a relativistic kinetic theory for phonon gases in superfluids, deriving macroscopic equations from microscopic particle dynamics and analyzing how phonons influence superfluid properties, including the speed of sound.

Contribution

It introduces a relativistic kinetic framework for superfluid phonons, linking microscopic quasi-particle dynamics to macroscopic superfluid behavior, and addresses phonon effects on sound speed.

Findings

Derived macroscopic balance equations from microscopic phonon dynamics.

Established relations between phonon contributions and superfluid parameters.

Solved the relativistic variation of the speed of sound due to phonons at low temperature.

Abstract

The relativistic kinetic theory of the phonon gas in superfluids is developed. The technique of the derivation of macroscopic balance equations from microscopic equations of motion for individual particles is applied to an ensemble of quasi-particles. The necessary expressions are constructed in terms of a Hamilton function of a (quasi-)particle. A phonon contribution into superfluid dynamic parameters is obtained from energy-momentum balance equations for the phonon gas together with the conservation law for superfluids as a whole. Relations between dynamic flows being in agreement with results of relativistic hydrodynamic consideration are found. Based on the kinetic approach a problem of relativistic variation of the speed of sound under phonon influence at low temperature is solved.