The thermalization of soft modes in non-expanding isotropic quark gluon plasmas

We discuss the role of elastic and inelastic collisions and their interplay in the thermalization of the quark-gluon plasma. We consider a simplified situation of a static plasma, spatially uniform and isotropic in momentum space. We focus on the small momentum region, which equilibrates first, and on a short time scale. We obtain a simple kinetic equation that allows for an analytic description of the most important regimes. The present analysis suggests that the formation of a Bose condensate, expected when only elastic collisions are present, is strongly hindered by the inelastic, radiative, processes.