  We consider the quantum Boltzmann equation, which describes the growth of the
condensate, or in other words, models the interaction between excited atoms and
a condensate. In this work, the full form of Bogoliubov dispersion law is
considered, which leads to a detailed study of surface integrals inside the
collision operator on energy manifolds. We prove that positive radial solutions
of the quantum Boltzmann equation are bounded from below by a Gaussian,
uniformly in time.
