Dynamical formation of a Bose-Einstein condensate

We explain how a condensate forms in finite time by a selfsimilar blow-up of the solution of the relevant quantum Boltzmann kinetic equation for a dilute quantum Bose gas. The condensate, once it is there, keeps exchanging mass with the rest of the distribution until equilibrium is reached, as described by a version of the kinetic equation that includes the existence of this condensate.