Sound Propagation in Cigar-Shaped Bose Liquids in the Thomas-Fermi Approximation: A Comparative Study between Gross-Pitaevskii and Logarithmic Models

A comparative study is conducted 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 demonstrated 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 demonstrated 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.

Automated summary

A comparative study is conducted to analyze the propagation of sound pulses in elongated Bose liquids and Bose-Einstein condensates using the Gross-Pitaevskii and logarithmic models. The study shows that the propagation of small density fluctuations is essentially one-dimensional in both models. It also reveals that the speed of sound scales differently in the two cases, with a square root dependence on particle density in the Gross-Pitaevskii liquid/condensate case and a constant value in the homogeneous logarithmic liquid case.