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

TL;DR

This paper investigates the spectral properties of SU(3) gauge theories, revealing universal eigenvalue behaviors, fractal eigenstates near the chiral transition, and estimating thermalization times in non-equilibrium QCD states.

Contribution

It introduces a gauge-invariant spectral analysis method for non-Abelian gauge theories and links eigenstate properties to thermalization and phase transition universality.

Findings

Eigenvalues below the magnetic scale resemble Gaussian Unitary ensemble statistics.

Fractal-like eigenstate clusters emerge near the chiral crossover.

Estimated thermalization time is approximately 1.44 fm/c.

Abstract

We study some interesting aspects of the spectral properties of SU(3) gauge theory, both with and without dynamical quarks (QCD) at thermal equilibrium using lattice gauge theory techniques. By calculating the eigenstates of a massless overlap Dirac operator on the gauge configurations, we implement a gauge-invariant method to study spectral properties of non-Abelian gauge theories. We have unambiguously categorized Dirac eigenvalues into different regimes based on a quantity defined in terms of the ratios of nearest neighbor spacings. While majority of these eigenstates below the magnetic scale are similar to those of random matrices belonging to the Gaussian Unitary ensemble at temperatures much higher than the chiral crossover transition in QCD, a few among them start to become prominent only near the crossover. These form fractal-like clusters with the median value for their fractal dimensions hinting at the universality class of the chiral transition in QCD. We further demonstrate that momentum modes below the magnetic scale in a particular non-equilibrium state of QCD are classically chaotic and estimate an upper bound on the thermalization time $\sim 1.44$ fm/c by matching this magnetic scale with that of a thermal state at $\sim 600$ MeV.