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arXiv · 2510.14886

Ruelle-Pollicott Decay of Out-of-Time-Order Correlators in Many-Body Systems

Jerónimo Duarte·Ignacio García-Mata·Diego A. Wisniacki
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Abstract

The out-of-time-order correlator (OTOC) quantifies information scrambling in quantum systems and serves as a key diagnostic of quantum chaos. In one-body systems with a classical counterpart, the relaxation of the OTOC is governed by Ruelle-Pollicott resonances. For many-body systems lacking a semiclassical limit, recent studies have identified an analogous role played by the Liouvillian spectrum of weakly open extensions of the dynamics, where the slowest decay rate -- the Liouvillian gap -- encodes relaxation. Here we study the kicked Ising spin chain and show that the long-time exponential decay of the OTOC in the isolated system occurs at a rate equal to twice this intrinsic gap. This correspondence is demonstrated across parameter regions exhibiting distinct level spacing statistics, indicating that the Liouvillian spectrum provides a robust framework for characterizing relaxation and irreversibility in closed many-body quantum systems.

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Jerónimo Duarte, Ignacio García-Mata, Diego A. Wisniacki. 2025-10-16. Ruelle-Pollicott Decay of Out-of-Time-Order Correlators in Many-Body Systems. https://doi.org/10.1103/5rlf-93y8

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