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Title:
Analytical results for the evolution of chaotic many-body quantum systems
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Abstract:
Possible strategies to describe analytically the dynamics of many-body quantum systems out of equilibrium include the use of integrable models and of full random matrices. They provide bounds and serve as references for the studies of systems investigated experimentally. We take the path of random matrices and obtain analytical expressions for the survival probability, density imbalance, and out-of-time-ordered correlator. Using these findings, we propose an expression that matches very well numerical results for the evolution of realistic disordered spin-1/2 models that are strongly chaotic and quenched far from equilibrium. By comparing the outcomes from the random matrix and spin models, a late power-law behavior followed by the so-called correlation hole are identified as generic features of chaotic many-body quantum systems. The power-law exponent and depth of the hole are then employed in the analysis of the transition from chaos to localization, which occurs as the disorder strength of the spin model increases.
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