Density excitations of a harmonically trapped ideal gas

TL;DR

This paper calculates the dynamic and static structure factors of a harmonically trapped ideal Bose gas above the condensation temperature, revealing temperature-dependent density fluctuations and differences based on particle number.

Contribution

It provides a detailed analysis of density excitations in a trapped ideal gas, including the effects of a phenomenological relaxation mechanism and particle number variations.

Findings

Static structure factor vanishes as wavenumber squared at long wavelengths

Dynamic structure factor shows significant temperature dependence

Debye-Waller factor varies with wavenumber and particle number

Abstract

The dynamic structure factor of a harmonically trapped Bose gas has been calculated well above the Bose-Einstein condensation temperature by treating the gas cloud as a canonical ensemble of noninteracting classical particles. The static structure factor is found to vanish as wavenumber squared in the long-wavelength limit. We also incorporate a relaxation mechanism phenomenologically by including a stochastic friction force to study the dynamic structure factor. A significant temperature dependence of the density-fluctuation spectra is found. The Debye-Waller factor has been calculated for the trapped thermal cloud as function of wavenumber and of particle number. A substantial difference is found between clouds of small and large particle number.