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

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.