Varikuti Naga Dileep, Sahu Abinash, Lakshminarayan Arul, Madhok Vaibhav
Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India and Center for Quantum Information, Communication and Computation, Indian Institute of Technology Madras, Chennai 600036, India.
Phys Rev E. 2024 Jan;109(1-1):014209. doi: 10.1103/PhysRevE.109.014209.
Non-Kolmogorov-Arnold-Moser (KAM) systems, when perturbed by weak time-dependent fields, offer a fast route to classical chaos through an abrupt breaking of invariant phase-space tori. In this work, we employ out-of-time-order correlators (OTOCs) to study the dynamical sensitivity of a perturbed non-KAM system in the quantum limit as the parameter that characterizes the resonance condition is slowly varied. For this purpose, we consider a quantized kicked harmonic oscillator (KHO) model, which displays stochastic webs resembling Arnold's diffusion that facilitate large-scale diffusion in the phase space. Although the Lyapunov exponent of the KHO at resonances remains close to zero in the weak perturbative regime, making the system weakly chaotic in the conventional sense, the classical phase space undergoes significant structural changes. Motivated by this, we study the OTOCs when the system is in resonance and contrast the results with the nonresonant case. At resonances, we observe that the long-time dynamics of the OTOCs are sensitive to these structural changes, where they grow quadratically as opposed to linear or stagnant growth at nonresonances. On the other hand, our findings suggest that the short-time dynamics remain relatively more stable and show the exponential growth found in the literature for unstable fixed points. The numerical results are backed by analytical expressions derived for a few special cases. We will then extend our findings concerning the nonresonant cases to a broad class of near-integrable KAM systems.
非柯尔莫哥洛夫 - 阿诺德 - 莫泽（KAM）系统在受到弱时间依赖场扰动时，通过不变相空间环面的突然破裂提供了一条通向经典混沌的快速途径。在这项工作中，我们使用非时序关联函数（OTOCs）来研究一个受扰非KAM系统在量子极限下的动力学敏感性，其中表征共振条件的参数是缓慢变化的。为此，我们考虑一个量子化的受驱谐振子（KHO）模型，它展示出类似于阿诺德扩散的随机网，这有助于在相空间中进行大规模扩散。尽管在弱微扰 regime 下，KHO 在共振时的李雅普诺夫指数仍接近零，使得系统在传统意义上是弱混沌的，但经典相空间会经历显著的结构变化。受此启发，我们研究系统处于共振时的 OTOCs，并将结果与非共振情况进行对比。在共振时，我们观察到 OTOCs 的长时间动力学对这些结构变化敏感，它们呈二次方增长，这与非共振时的线性或停滞增长形成对比。另一方面，我们的发现表明，短时间动力学相对更稳定，并显示出文献中针对不稳定不动点所发现的指数增长。数值结果得到了针对一些特殊情况推导的解析表达式的支持。然后，我们将把关于非共振情况的发现扩展到一类广泛的近可积 KAM 系统。
