Hard gluon evolution in warming medium

We describe the energy distribution of hard gluons travelling through a dense quark-gluon plasma whose temperature increases linearly with time, within a probabilistic perturbative approach. The results were applied to the thermalization problem in heavy ion collisions. In the weak coupling picture this thermalization occurs from "the bottom up": high energy partons, formed early in the collision, radiate low energy gluons which then proceed to equilibrate among themselves, forming a thermal bath that brings the high energy sector to equilibrium. We see that, in this scenario, the dynamic we describe must set in around t similar to 0.5 fm/c after the collision in order to reach a fully thermalized state at t similar to 1 fm/c. We then look at the entropy density and average temperature of the soft thermal bath, as the system approaches (local) thermal equilibrium.