Title: Ruelle-Pollicott Decay of Out-of-Time-Order Correlators in Many-Body Systems Show Chinese title

Title: Ruelle-Pollicott 传播子在多体系统中的非时序关联函数衰减

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. Show Chinese abstract

Abstract: 量子系统中信息的混乱程度由非时间顺序关联函数（OTOC）来量化，并且它是量子混沌的关键诊断工具。在具有经典对应物的一体系统中，OTOC的弛豫由Ruelle-Pollicott共振所支配。对于缺乏半经典极限的多体系统，最近的研究发现，弱开放动力学扩展的Liouvillian谱扮演了类似的角色，其中最慢的衰减率——Liouvillian间隙——编码了弛豫。在这里，我们研究了受激伊辛自旋链，并表明孤立系统中OTOC的长时间指数衰减速率等于这个内在间隙的两倍。这种对应关系甚至在可积性与混沌之间的过渡区域也持续存在，证明Liouvillian谱为理解封闭多体量子系统的弛豫和不可逆性提供了一个统一的框架。