Weakly interacting Bose-Einstein condensates in temperature-dependent generic traps

We study the shift ΔTc in the condensation temperature of an atomic Bose-Einstein condensate trapped in a temperature-dependent three-dimensional generic potential. With no assumptions other than the mean-field approach and the semiclassical approximation, it is shown that the inclusion of a T-dependent trap improves upon the pure semiclassical result giving better agreement between the predicted ΔTc value and its experimental value. However, despite this improvement, the effect of a T-dependent trap is not sufficient to fully reduce the discrepancy between theoretical prediction and data.