We consider a system of two coupled oscillators one of which is driven parametrically and investigate both classical and quantum dynamics within Floquet description. Characteristic changes in the time evolution of the quantum fluctuations are observed for dynamically stable and unstable regions. Dynamical instability generated by the parametrically driven oscillator leads to infinite temperature thermalization of the undriven oscillator which is evident from the equi-partitioning of energy, reduced density matrix and saturation of entanglement entropy. We also confirm that the classical Lyapunov exponent is correctly captured from the growth rate of `unequal time commutator' of dynamical variables which indicates thermalization stems from the instability in quantum system.

中文翻译：

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参数驱动耦合振荡器中的热化

我们考虑一个由两个耦合振荡器组成的系统，其中一个是参数驱动的，并在 Floquet 描述中研究经典动力学和量子动力学。对于动态稳定和不稳定区域，观察到量子涨落随时间演化的特征变化。参数驱动振荡器产生的动态不稳定性导致未驱动振荡器的无限温度热化，这从能量的均分、密度矩阵减小和纠缠熵的饱和中可以明显看出。我们还证实，经典的李雅普诺夫指数是从动态变量的“不等时换向器”的增长率中正确捕获的，这表明热化源于量子系统的不稳定性。