Nonequilibrium field theory description of the Bose-Einstein condensate

We study the detailed out-of-equilibrium time evolution of a homogeneous Bo se-Einstein condensate (BEC). We consider a nonrelativistic quantum theory for a self-interacting complex scalar field, immersed in a thermal bath, as an effective microscopic model for the description of the BEG. The interac tion between fluctuations proves to be crucial in the mechanism of instabil ity generation. We show the existence of two regimes in k space, with a cro ssover for k(2)/2m similar to 2 lambda\phi(0)\(2), where lambda is the coup ling constant and \phi(0)\(2) is the condensate density. We deduce and solv e a set of coupled equations that completely determines the nonequilibrium dynamics of the condensate density.