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 $\sim Q_s$. 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 analyze 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 ${\gamma }^{-1}\simeq 1–2\mathrm{fm}/\mathrm{c}$ for coarse-graining momentum scales of $p\lesssim 1\mathrm{GeV}$ choosing an initial energy density for RHIC of $ϵ=30\mathrm{GeV}/{\mathrm{fm}}^3$. The nonequilibrium spatial Wilson loop is found to exhibit an area law and to become isotropic on a similar time scale.

• Received 21 December 2007

DOI:https://doi.org/10.1103/PhysRevD.77.034504