First sound velocity in liquid $^{4}$He

TL;DR

This paper derives the temperature dependence of the first sound velocity in liquid helium-4 using a many-boson model that includes multi-particle correlations, aligning with known limits and aiding in understanding helium's thermodynamics.

Contribution

It introduces a new expression for sound velocity in liquid helium-4 that incorporates three- and four-particle correlations within the post-RPA approximation.

Findings

The derived sound velocity expression matches known low and high temperature limits.

The results facilitate analysis of multi-particle correlation contributions.

The approach improves understanding of thermodynamic features of liquid helium-4.

Abstract

Based on the many-boson system structure factor, which takes into account three- and four-particle direct correlations, there was found the first sound velocity temperature behaviour in liquid $^4$He in the post-RPA approximation. The expression received for the sound velocity matches with the well-known results in both low and high temperature limits. The results of this paper can be used to analyze the contributions of three- and four-particle correlations into thermodynamic and structural features of liquid $^4$He.