Dirac mass formation in kinetic equations for quantum particles

We shall consider the kinetic equation describing the Compton scattering interaction between electrons and photons. We will see that the solutions may concentrate at the origin and form a Dirac mass assymptotically as $t$ tends to infinity. This is a sort of Bose condensation in infinite time. We will describe precisely the formation of the Dirac mass and show that it is of self similar form and strongly depends on the behavior of the initial data near the origin.