Time-series analysis and network analysis are now used extensively in diverse areas of science. In this paper, we applythese techniques to quantum dynamics in an optomechanical system: specifically, the long-time dynamics of the mean photon number in an archetypal tripartite quantum system comprising a single-mode radiation field interacting with a two-level atom and an oscillating membrane. We also investigate a classical system of interacting Duffing oscillators which effectively mimics several of the features of tripartite quantum-optical systems. In both cases, we examine the manner in which the maximal Lyapunov exponent obtained from a detailed time-series analysis varies with changes in an appropriate tunable parameter of the system. Network analysis is employed in both the quantum and classical models to identify suitable network quantifiers which will reflect these variations with the system parameter. This is a novel approach towards (i) examining how a considerably smaller data set (the network) obtained from a long time series of dynamical variables captures important aspects of the underlying dynamics, and (ii) identifying the differences between classical and quantum dynamics.

中文翻译：

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量子动力学中的时间序列和网络分析：与经典动力学的比较

时间序列分析和网络分析现在广泛用于不同的科学领域。在本文中，我们将这些技术应用于光机械系统中的量子动力学：具体而言，原型三方量子系统中平均光子数的长期动力学，包括与两能级原子相互作用的单模辐射场和振荡膜。我们还研究了一个经典的相互作用的杜芬振荡器系统，它有效地模仿了三方量子光学系统的几个特征。在这两种情况下，我们检查从详细的时间序列分析中获得的最大李雅普诺夫指数随系统适当可调参数的变化而变化的方式。量子模型和经典模型都采用网络分析来确定合适的网络量词，这些量词将反映这些随系统参数的变化。这是一种新颖的方法，用于 (i) 检查从长期动态变量序列中获得的相当小的数据集（网络）如何捕获潜在动力学的重要方面，以及 (ii) 确定经典动力学和量子动力学之间的差异。