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. 
R. Bach, M. Brewczyk, K. Rzazewski