  We consider in this paper a system coupling a linear quantum Boltzmann
equation and a defocusing cubic nonlinear Schrodinger equation. The Schrodinger
equation reflects the dynamics of the wave function of the Bose-Einstein
Condensate and the kinetic part of the system describes the evolution of the
density function of the thermal cloud. An existence and uniqueness result for
the system is supplied. We also prove the convergence to equilibrium of the
density function of the thermal cloud and a scattering theory for the wave
function of the condensate.
