Instabilities of an anisotropically expanding non-Abelian plasma:1D+3Vdiscretized hard-loop simulations

Abstract

Non-Abelian plasma instabilities play a crucial role in the nonequilibrium dynamics of a weakly coupled quark-gluon plasma, and they importantly modify the standard perturbative bottom-up thermalization scenario in heavy-ion collisions. Using the auxiliary-field formulation of the hard-loop effective theory, we study numerically the real-time evolution of instabilities in an anisotropic collisionless Yang-Mills plasma undergoing longitudinal free-streaming expansion. In this first real-time lattice simulation we consider the most unstable modes, long-wavelength coherent color fields that are constant in transverse directions and which therefore are effectively 1+1 dimensional in space-time, except for the auxiliary fields which also depend on discretized momentum rapidity and transverse velocity components. We reproduce the semianalytical results obtained previously for the Abelian regime, and we determine the nonlinear effects which occur when the instabilities have grown such that non-Abelian interactions become important.