FINITE TEMPERATURE EXCITATIONS OF A TRAPPED BOSE-GAS

We present a detailed study of the temperature dependence of the conde nsate and noncondensate density profiles of a Bose-condensed gas in a parabolic trap. These quantities are calculated self-consistently usin g the Hartree-Fock-Bogoliubov equations within the Popov approximation . Below the Bose-Einstein transition the excitation frequencies have a relatively weak temperature dependence even though the condensate is strongly depleted. As the condensate density goes to zero through the transition, the excitation frequencies are strongly affected and appro ach the frequencies of a noninteracting trapped gas in the high temper ature limit.