Sound propagation in cigar-shaped Bose liquids in the Thomas-Fermi approximation: A comparative study between Gross-Pitaevskii and logarithmic models

TL;DR

This study compares sound pulse propagation in elongated Bose liquids using Gross-Pitaevskii and logarithmic models within the Thomas-Fermi approximation, revealing differences in how sound speed depends on particle density.

Contribution

It provides a comparative analysis of sound propagation in Bose liquids using two different models, highlighting their distinct behaviors in the linear regime.

Findings

Sound propagation is essentially one-dimensional in both models.

Sound speed scales with the square root of density in Gross-Pitaevskii model.

Sound speed remains constant in the logarithmic model.

Abstract

A comparative study is done of the propagation of sound pulses in elongated Bose liquids and Bose-Einstein condensates in Gross-Pitaevskii and logarithmic models, by means of the Thomas-Fermi approximation. It is shown that in the linear regime the propagation of small density fluctuations is essentially one-dimensional in both models, in the direction perpendicular to the cross section of a liquid's lump. Under these approximations, it is shown that the speed of sound scales as a square root of particle density in the case of the Gross-Pitaevskii liquid/condensate, but it is constant in a case of the homogeneous logarithmic liquid.