Temperature dependence of condensate fraction of weakly nonideal trapped Bose gas

Condensation of the weakly nonideal gas in an anisotropic parabolic trap was considered. The first order (with respect to the interaction parameter) correction $\Delta \bar n_0 = \bar n_0(T) - \bar n_0^0(T)$ to the temperature dependence of the ground state population $\bar n_0^0(T)$ of the ideal gas atoms was found using thermodynamic perturbation theory. The correction found $\Delta \bar n_0$ proved to be much larger than the one calculated within the mean field theory (see Giorgini S, Pitaevskii L P, Stringari S Phys. Rev. A 54 R4633 (1996)) at temperatures below critical. This correction tends to zero as the temperature approaches the critical one; i.e., the interaction of the atoms does not lead to variation in the critical temperature. A simple analytic expression was found that describes the smooth variation of $\bar n_0^0(T)$ as it approaches zero in the vicinity of the critical temperature. A new criterion for applicability of the thermodynamic limit is given.