Mechanism of collisionless sound damping in dilute Bose gas with condensate

TL;DR

This paper presents a microscopic theory for collisionless sound damping in dilute Bose gases with condensate, analyzing dispersion relations and damping rates across temperature regimes, highlighting differences from semi-phenomenological models.

Contribution

It develops a microscopic framework based on coupled evolution equations and Bogoliubov theory to analyze sound damping, providing new analytical and numerical results at various temperatures.

Findings

Derived dispersion equations for sound oscillations.

Obtained expressions for sound speed and damping rate.

Identified non-analytic temperature dependence effects.

Abstract

We develop a microscopic theory of sound damping due to Landau mechanism in dilute gas with Bose condensate. It is based on the coupled evolution equations of the parameters describing the system. These equations have been derived in earlier works within a microscopic approach which employs the Peletminskii-Yatsenko reduced description method for quantum many-particle systems and Bogoliubov model for a weakly nonideal Bose gas with a separated condensate. The dispersion equations for sound oscillations were obtained by linearization of the mentioned evolution equations in the collisionless approximation. They were analyzed both analytically and numerically. The expressions for sound speed and decrement rate were obtained in high and low temperature limiting cases. We have shown that at low temperature the dependence of the obtained quantities on temperature significantly differs from those obtained by other authors in the semi-phenomenological approaches. Possible effects connected with non-analytic temperature dependence of dispersion characteristics of the system were also indicated.