The dynamics of bose-einstein condensation

Abstract We study a non-linear integro-differential equation describing the evolution of a gas of Bosons interacting with a heat bath. The solution is shown to exist globally. A family of Liapunov functionals is constructed and used to prove convergence to equilibrium. The linearized equation determines a semi-group of contractions. The nature of approach to equilibrium (exponential at low density, but not in the two-phase region) is studied in relation to the spectral properties of the generator of the semi-group.