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 ${\tau }_{\mathrm{eq}}\sim 2\pi /T$ 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.

Comments: 10 pages, 8 figures; (v2) version accepted for publication in PRD