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

• URL: http://arxiv.org/abs/2011.09814v2
• Date: Tue, 11 May 2021 01:30:57 GMT
• Title: Thermalization of Yang-Mills theory in a $(3+1)$ dimensional small lattice system
• Authors: Tomoya Hayata, Yoshimasa Hidaka
• Abstract summary: We numerically solve the Schr"odinger equation with the Kogut-Susskind Hamiltonian. We observe the thermalization of a Wilson loop to the canonical state.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 Schr{\"o}dinger 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 $\tau_{\rm eq}\sim 2\pi/T$ 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.

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