Abstract
We prove existence and uniqueness of the solution of a homogeneous quantum Boltzmann equation describing the photon–electron interaction. We study the asymptotic behaviour of the solutions, and show in particular, that the photon density distribution condensates at the origin asymptotically in time when the total number of photons is larger than a given positive constant. We also recover the Kompaneets equation as a Fokker–Planck type limit of this Boltzmann model.
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