Formation of the condensate in a dilute Bose gas

We examine the time evolution of a weakly interacting Bose gas in the course of the Bose-Einstein phase transition and show that, in contrast with previous claims in the literature, the relevant time scale for the appearance of the condensate is finite and, under the conditions we consider, of O(ħ/${\mathit{k}}_{\mathit{B}}$ ${\mathit{T}}_{\mathit{c}}$), which is very small compared to the characteristic lifetime of the system due to inelastic collisions in the gas.