Thermalization of Yang-Mills theory in a (3+1)-dimensional small lattice system

Abstract

We study the real-time evolution of SU(2) Yang-Mills theory in a (3+1)-dimensional small lattice system after interaction quench. We numerically solve the Schrödinger equation with the Kogut-Susskind Hamiltonian in the physical Hilbert space obtained by solving Gauss law constraints. We observe the thermalization of a Wilson loop to the canonical state; the relaxation time is insensitive to the coupling strength and estimated as τeq∼2π/T with temperatures T at steady states. We also compute the vacuum persistence probability (the Loschmidt echo) to understand the relaxation from the dynamics of the wave function.