Understanding thermalization in a non-Abelian gauge theory

Understanding the mechanism of thermalization in gauge theories is one of the challenging problems of contemporary research. In this talk, I will discuss about our recent work where we characterize the spectral properties of a strongly-interacting system in thermal equilibrium described by Quantum Chromodynamics calculated using lattice field theory techniques, in terms of robust observables which depend on ratios of level spacings between the Dirac eigenvalues. Whereas low-lying eigenvectors are fractal-like near the chiral crossover transition, at higher temperatures almost all eigenvalues below the non-perturbative magnetic scale have properties similar to a particular random matrix theory, signaling chaotic behavior. By matching this scale between a thermal and a particular non-equilibrium chaotic state of QCD, we provide a first estimate of thermalization time $\sim 1.44$ fm/c. We also extract the Lyapunov exponents characterizing the chaotic nature of non-Abelian gauge theory in the non-equilibrium state as well as in a high temperature equilibrium state. Using them we provide another independent estimate of the thermalization time of the magnetic modes and discuss the implications of our study.