Approach to Equilibrium in Weakly Coupled Non-Abelian Plasmas

We follow the time evolution of non-Abelian gauge bosons from far-from-equilibrium initial conditions to thermal equilibrium by numerically solving an effective kinetic equation that becomes accurate in the weak coupling limit. We consider isotropic initial conditions that are either highly overoccupied or underoccupied. We find that overoccupied systems thermalize through a self-similar cascade reaching equilibrium in multiples of a thermalization time t(eq)≈72./(1+0.12logλ(-1))×1/λ(2)T, whereas underoccupied systems undergo a "bottom-up" thermalization in a time t(eq)≈34.+21.log(Q/T)/(1+0.037logλ(-1))×(Q/T)(1/2)/λ(2)T, where Q is the characteristic momentum scale of the initial condition. We apply this result to model initial stages of heavy-ion collisions and find rapid thermalization roughly in a time Qt(eq)≲10 or t(eq)≲1 fm/c.