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

• URL: http://arxiv.org/abs/2510.14886v2
• Date: Mon, 20 Oct 2025 20:04:39 GMT
• Title: Ruelle-Pollicott Decay of Out-of-Time-Order Correlators in Many-Body Systems
• Authors: Jerónimo Duarte, Ignacio García-Mata, Diego A. Wisniacki,
• Abstract summary: We show that the long-time exponential decay of the OTOC in the isolated system occurs at a rate equal to twice this intrinsic gap.<n>This correspondence persists even in crossover regimes between integrability and chaos.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 persists even in crossover regimes between integrability and chaos, demonstrating that the Liouvillian spectrum provides a unified framework for understanding relaxation and irreversibility in closed many-body quantum systems.

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