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arXiv · 2411.16274

Out-of-Time Ordered Correlator for a Chaotic Many-Body Quantum System

Hans A. Weidenmüller
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Abstract

Using the parametric representation of a chaotic many-body quantum system derived earlier, we calculate explicitly the large-time dependence and asymptotic value of the out-of-time correlator (OTOC) of that system. The dependence on time $t$ is determined by $\Delta t / \hbar$. Here $\Delta$ is the energy correlation width within which the Bohigas-Giannoni-Schmit conjecture applies. We conjecture that $\Delta$ is universally related to the leading Ljapunov coefficient of the corresponding classical system by $\Delta = \hbar \lambda_{\max}$. Then the large-time behavior of OTOC is given by the dimensionless parameter $\lambda_{\max} t$.

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Hans A. Weidenmüller. 2024-11-25. Out-of-Time Ordered Correlator for a Chaotic Many-Body Quantum System. https://arxiv.org/abs/2411.16274

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