Kinetic equations for Bose-Einstein condensates from the 2PI effective action

Abstract

We use the 2PI effective action of a relativistic scalar field theory to derive kinetic equations for a Bose-condensed system near the phase transition.We start from equations of motion derived within a 1/N-expansion at NLO. In taking the non-relativistic limit we obtain a generalized Gross-Pitaevskii equation for the condensate field. Within the Popov approximation we explicitly compute the collision term up to order g^2 using the Kadanoff-Baym formalism. For the sake of self-consistency we derive in the same way a Boltzmann equation for the non-condensate distribution function. The final results are in agreement to those previously obtained by Griffin, Nikuni and Zaremba and by Stoof.