Finite Temperature Perturbation Theory for a Spatially Inhomogeneous Bose-condensed Gas

TL;DR

This paper develops a finite temperature perturbation theory for inhomogeneous Bose-condensed gases, enabling calculation of damping rates and energy shifts of excitations, with applications to trapped gases and sound propagation.

Contribution

It introduces a generalized perturbation theory for inhomogeneous Bose gases, accounting for spatial density variations and boundary effects, extending beyond mean-field approximations.

Findings

Damping rates and energy shifts differ significantly in inhomogeneous versus homogeneous gases.

Boundary regions critically influence low-energy excitation properties.

The theory explains damping phenomena observed in recent experiments.

Abstract

We develop a finite temperature perturbation theory (beyond the mean field) for a Bose-condensed gas and calculate temperature-dependent damping rates and energy shifts for Bogolyubov excitations of any energy. The theory is generalized for the case of excitations in a spatially inhomogeneous (trapped) Bose-condensed gas, where we emphasize the principal importance of inhomogeneouty of the condensate density profile and develop the method of calculating the self-energy functions. The use of the theory is demonstrated by calculating the damping rates and energy shifts of low-energy quasiclassical excitations, i.e. the quasiclassical excitations with energies much smaller than the mean field interaction between particles. In this case the boundary region of the condensate plays a crucial role, and the result for the damping rates and energy shifts is completely different from that in spatially homogeneous gases. We also analyze the frequency shifts and damping of sound waves in cylindrical Bose condensates and discuss the role of damping in the recent MIT experiment on the sound propagation.