Acoustic oscillations in cigar-shaped logarithmic Bose-Einstein condensate in the Thomas-Fermi approximation

TL;DR

This paper investigates the behavior of density fluctuations and oscillations in a cigar-shaped logarithmic Bose-Einstein condensate, revealing how nonlinear coupling influences wave propagation, density, and energy in anisotropic traps.

Contribution

It introduces a detailed analysis of density fluctuations in logarithmic BECs using the Thomas-Fermi approximation, highlighting the effects of nonlinear coupling on condensate dynamics.

Findings

Density fluctuations propagate as one-dimensional waves along the trap axis.

Sign of nonlinear coupling determines whether fluctuations form pulses, standing waves, or oscillations.

Density and energy behaviors depend critically on the sign and magnitude of nonlinear coupling.

Abstract

We consider the dynamical properties of density fluctuations in the cigar-shaped Bose-Einstein condensate described by the logarithmic wave equation with a constant nonlinear coupling by using the Thomas-Fermi and linear approximations. It is shown that the propagation of small density fluctuations along the long axis of a condensed lump in a strongly anisotropic trap is essentially one-dimensional, while the trapping potential can be disregarded in the linear regime. Depending on the sign of nonlinear coupling, the fluctuations either take the form of translationally symmetric pulses and standing waves, or become oscillations with varying amplitudes. We also study the condensate in an axial harmonic trap, by using elasticity theory's notions. Linear particle density and energy also behave differently depending on the nonlinear coupling's value. If it is negative, the density monotonously grows along with lump's radius, while energy is a monotonous function of density. For the positive coupling, the density is bound from above, whereas energy grows monotonously as a function of density until it reaches its global maximum.