Approach to equilibrium in weakly coupled nonabelian plasmas

TL;DR

This paper models the thermalization process of nonabelian gauge bosons in plasmas, revealing different timescales for overoccupied and underoccupied initial conditions, with applications to heavy-ion collision dynamics.

Contribution

It provides a numerical solution to an effective kinetic equation describing the thermalization of nonabelian plasmas, distinguishing between turbulent cascade and bottom-up mechanisms.

Findings

Overoccupied systems thermalize in approximately 72/(1-0.12 log λ)/λ² T.

Underoccupied systems undergo bottom-up thermalization with a timescale involving initial momentum scale Q.

Rapid thermalization occurs within about 1 fm/c in heavy-ion collision scenarios.

Abstract

We follow the time evolution of nonabelian 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 initial conditions that are either highly overoccupied or underoccupied. We find that overoccupied systems thermalize through a turbulent cascade reaching equilibrium in multiples of a thermalization time $t\approx 72./ (1-0.12\log \lambda)/\lambda^2 T$, whereas underoccupied systems undergo a "bottom-up" thermalization in a time $t\approx (34. +21. \ln(Q/T))/ (1-0.037\log \lambda)(Q/T)^{1/2}/\lambda^2 T$, 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 $Qt \lesssim 10$ or $t\lesssim 1$ fm/c.