Understanding the approach to thermalization from the eigenspectrum of non-Abelian gauge theories

We study the spectral properties of SU(3) gauge theory with and without dynamical quarks (QCD) at thermal equilibrium using lattice gauge theory techniques. By measuring eigenstates of a massless overlap Dirac operator on the gauge configurations, we provide a gauge invariant method to study spectral properties of non-Abelian gauge theories. Whereas the majority of these eigenstates below the magnetic scale have universal nearest-neighbor level spacing fluctuations consistent with certain class of random matrix theories at temperatures away from the chiral crossover transition in QCD, a few among them start to become prominent just above the crossover forming clusters percolating over the entire volume. By matching the non-perturbative magnetic scales in a high temperature thermal state and a particular non-equilibrium chaotic state of QCD, we provide an estimate of thermalization time ~ 1.44 fm/c.