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

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.

Automated summary

The study investigates the dynamical properties of density fluctuations in cigar-shaped Bose-Einstein condensates in different traps, showcasing that density fluctuations in strongly anisotropic traps are essentially one-dimensional and exhibit different forms of oscillations based on the sign of nonlinear coupling. Additionally, the behavior of linear particle density and energy varies depending on the value of the nonlinear coupling, affecting the growth patterns of density and energy in the system.