Finite temperature oscillations of a Bose-Einstein condensate in a two-gas model

The temperature dependence of the frequencies of a Bose-Einstein condensate obtained in experiment has not been fully understood theoretically. In this paper we present a simplified version of a two-gas model. A numerically-found ground state of the system is used for the small-oscillations analysis. In the case of spherical symmetry a full spectrum of frequencies is found for low orbital quantum numbers. Avoided crossings that appear in the spectrum might be the reason for experimentally observed frequency shifts.