Hydrodynamic modes in a trapped Bose gas above the Bose-Einstein transition

TL;DR

This paper analyzes the collective hydrodynamic modes of a trapped Bose gas above the Bose-Einstein transition, deriving explicit solutions and comparing surface mode dispersion with zero-temperature condensate oscillations.

Contribution

It derives a closed equation for velocity fluctuations in a trapped Bose gas above the transition, providing explicit solutions and connecting surface modes to zero-temperature condensate oscillations.

Findings

Surface modes share dispersion with zero-temperature condensate oscillations.

Explicit solutions for monopole and coupled modes are provided.

Results enhance understanding of collective excitations above BEC transition.

Abstract

We discuss the collective modes of a trapped Bose gas in the hydrodynamic regime where atomic collisions ensure local thermal equilibrium for the distribution function. Starting from the conservation laws, in the linearized limit we derive a closed equation for the velocity fluctuations in a trapped Bose gas above the Bose-Einstein transition temperature. Explicit solutions for a parabolic trap are given. We find that the surface modes have the same dispersion relation as the one recently obtained by Stringari for the oscillations of the condensate at $T=0$ within the Thomas-Fermi approximation. Results are also given for the monopole ``breathing'' mode as well as for the $m=0$ excitations which result from the coupling of the monopole and quadrupole modes in an anisotropic parabolic well.