论文标题
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
Time-series and network analysis in quantum dynamics: Comparison with classical dynamics
论文作者
论文摘要
现在，时间序列分析和网络分析已广泛用于科学的不同领域。在本文中，我们将这些技术应用于光学机械系统中的量子动力学：具体来说，在原型三方量子系统中，平均光子数的长期动力学包括一个包含单模辐射场，该量子与两级原子相互作用和振荡膜。我们还研究了一种相互作用的悬挂振荡器的经典系统，该系统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，我们都会研究从详细的时间序列分析获得的最大Lyapunov指数的方式，随着系统的适当可调参数的变化而变化。网络分析在量子和经典模型中均采用了合适的网络量词，这将用系统参数反映这些变化。这是一种新颖的方法（i）检查从长时间的动态变量序列中获得的相当小的数据集（网络）如何捕获基本动力学的重要方面，以及（ii）识别经典动力学和量子动力学之间的差异。
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.
