Gapless finite-$T$ theory of collective modes of a trapped gas

Abstract

We present predictions for the frequencies of collective modes of trapped Bose-condensed ${}^{87}$Rb atoms at finite temperature. Our treatment includes a self-consistent treatment of the mean-field from finite-$T$ excitations and the anomolous average. This is the first gapless calculation of this type for a trapped Bose-Einstein condensed gas. The corrections quantitatively account for the downward shift in the $m=2$ excitation frequencies observed in recent experiments as the critical temperature is approached.

4 pages Latex and 2 postscript figures