Varikuti Naga Dileep, Madhok Vaibhav
Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India and Center for Quantum Information, Communication and Computing (CQuICC), Indian Institute of Technology Madras, Chennai 600036, India.
Chaos. 2024 Jun 1;34(6). doi: 10.1063/5.0191140.
We study operator growth in a bipartite kicked coupled tops (KCTs) system using out-of-time ordered correlators (OTOCs), which quantify "information scrambling" due to chaotic dynamics and serve as a quantum analog of classical Lyapunov exponents. In the KCT system, chaos arises from the hyper-fine coupling between the spins. Due to a conservation law, the system's dynamics decompose into distinct invariant subspaces. Focusing initially on the largest subspace, we numerically verify that the OTOC growth rate aligns well with the classical Lyapunov exponent for fully chaotic dynamics. While previous studies have largely focused on scrambling in fully chaotic dynamics, works on mixed-phase space scrambling are sparse. We explore scrambling behavior in both mixed-phase space and globally chaotic dynamics. In the mixed-phase space, we use Percival's conjecture to partition the eigenstates of the Floquet map into "regular" and "chaotic." Using these states as the initial states, we examine how their mean phase space locations affect the growth and saturation of the OTOCs. Beyond the largest subspace, we study the OTOCs across the entire system, including all other smaller subspaces. For certain initial operators, we analytically derive the OTOC saturation using random matrix theory (RMT). When the initial operators are chosen randomly from the unitarily invariant random matrix ensembles, the averaged OTOC relates to the linear entanglement entropy of the Floquet operator, as found in earlier works. For the diagonal Gaussian initial operators, we provide a simple expression for the OTOC.
我们使用非时序关联函数（OTOCs）研究二分踢耦合陀螺（KCTs）系统中的算符增长，OTOCs量化了由于混沌动力学导致的“信息搅乱”，并作为经典李雅普诺夫指数的量子类似物。在KCT系统中，混沌源于自旋之间的超精细耦合。由于一个守恒定律，系统动力学分解为不同的不变子空间。最初聚焦于最大的子空间，我们通过数值验证了对于完全混沌动力学，OTOC增长率与经典李雅普诺夫指数吻合良好。虽然先前的研究主要集中在完全混沌动力学中的搅乱，但关于混合相空间搅乱的研究很少。我们探索混合相空间和全局混沌动力学中的搅乱行为。在混合相空间中，我们使用珀西瓦尔猜想将弗洛凯映射的本征态划分为“规则”和“混沌”。以这些态作为初始态，我们研究它们的平均相空间位置如何影响OTOCs的增长和饱和。在最大子空间之外，我们研究整个系统的OTOCs，包括所有其他较小的子空间。对于某些初始算符，我们使用随机矩阵理论（RMT）解析推导OTOC饱和。当从酉不变随机矩阵系综中随机选择初始算符时，如早期工作中所发现的，平均OTOC与弗洛凯算符的线性纠缠熵相关。对于对角高斯初始算符，我们给出了OTOC的一个简单表达式。
