Thermalization in Weakly Coupled Nonabelian Plasmas

TL;DR

This paper analyzes how weakly coupled nonabelian plasmas, both isotropic and anisotropic, approach equilibrium, providing parametric estimates for equilibration times based on initial conditions and anisotropy levels.

Contribution

It offers a comprehensive parametric study of thermalization times in nonabelian plasmas considering various initial distributions and anisotropies, extending understanding of equilibration dynamics.

Findings

Equilibration time scales depend on initial temperature, momentum, and anisotropy.

Isotropic systems equilibrate in a time proportional to /T or  Q^{1/2} T^{-3/2}.

Anisotropic systems can equilibrate faster under certain conditions.

Abstract

We investigate how relativistic, nonabelian plasmas approach equilibrium in a general context. Our treatment is entirely parametric and for small Yang-Mills coupling $\alpha$. First we study isotropic systems with an initially nonequilibrium momentum distribution. We consider both the case of initially very high occupancy and initially very low occupancy. Then we consider systems which are anisotropic. We consider both weak anisotropy and large anisotropy, and allow the occupancy to be parametrically large or small. Writing the typical momentum of an initial excitation as Q and the final temperature as T, full equilibration occurs in a time t ~ \alpha^{-2}/T for T > Q, and t ~ \alpha^{-2} Q^{1/2} T^{-3/2} for T < Q, unless the initial system is sufficiently anisotropic and T > \alpha^{2/3} Q, in which case equilibration occurs somewhat faster, t ~ \alpha^{-13/7} Q^{5/7} T^{-12/7} (or \alpha^{-2}/T if that is longer).