Bottom-up isotropization in classical-statistical lattice gauge theory

TL;DR

This study investigates the early thermalization process in heavy-ion collisions using classical-statistical lattice gauge theory, revealing bottom-up isotropization and growth of instabilities in SU(2) gauge fields.

Contribution

It demonstrates the isotropization process in classical SU(2) gauge theory with anisotropic initial conditions, including the analysis of primary and secondary instabilities beyond the hard-loop approximation.

Findings

Primary instabilities with growth rates similar to weak coupling predictions.

Secondary growth rates reach larger values at higher momenta.

Pressure isotropizes within 1-2 fm/c, and Wilson loops become area law and isotropic.

Abstract

We compute nonequilibrium dynamics for classical-statistical SU(2) pure gauge theory on a lattice. We consider anisotropic initial conditions with high occupation numbers in the transverse plane on a characteristic scale ~ Q_s. This is used to investigate the very early stages of the thermalization process in the context of heavy-ion collisions. We find Weibel or "primary" instabilities with growth rates similar to those obtained from previous treatments employing anisotropic distributions of hard modes (particles) in the weak coupling limit. We observe "secondary" growth rates for higher-momentum modes reaching substantially larger values and we analyse them in terms of resummed loop diagrams beyond the hard-loop approximation. We find that a coarse grained pressure isotropizes "bottom-up" with a characteristic inverse rate of gamma^{-1} ~ 1 - 2 fm/c for coarse graining momentum scales of p < 1 GeV choosing an initial energy density for RHIC of epsilon = 30 GeV/fm^3. The nonequilibrium spatial Wilson loop is found to exhibit an area law and to become isotropic on a similar time scale.