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

We study the shift $\Delta T_{c}$ 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 $\Delta T_{c}$ 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.