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