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arXiv · 2308.02392

Refined quantum Lyapunov exponents from replica out-of-time-order correlators

Dmitrii A. Trunin
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Abstract

We suggest a new indicator of quantum chaos based on the logarithmic out-of-time-order correlator. On the one hand, this indicator correctly reproduces the average classical Lyapunov exponent in the semiclassical limit and directly links the definitions of quantum chaos and classical K-system. On the other hand, it can be analytically calculated using the replica trick and the Schwinger-Keldysh diagram technique on a $2n$-fold Keldysh contour. To illustrate this approach, we consider several one-dimensional systems, including the quantum cat map, and three paradigmatic large-$N$ models, including the Sachdev-Ye-Kitaev model. Furthermore, we find that correlations between replicas can reduce the magnitude of the Lyapunov exponent compared to estimates based on conventional out-of-time-order correlators.

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Dmitrii A. Trunin. 2023-11-16. Refined quantum Lyapunov exponents from replica out-of-time-order correlators. https://doi.org/10.1103/physrevd.108.105023

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