We study the effect of self-oscillation on the escape dynamics of classical and quantum open systems by employing the system-plus-environment-plus-interaction model. For a damped free particle (system) with memory kernel function expressed by Zwanzig (J. Stat. Phys. 9, 215 (1973)), which is originated from a harmonic oscillator bath (environment) of Debye type with cut-off frequency wd, ergodicity breakdown is found because the velocity autocorrelation function oscillates in cosine function for asymptotic time. The steady escape rate of such a self-oscillated system from a metastable potential exhibits nonmonotonic dependence on wd, which denotes that there is an optimal cut-off frequency makes it maximal. Comparing results in classical and quantum regimes, the steady escape rate of a quantum open system reduces to a classical one with wd decreasing gradually, and quantum fluctuation indeed enhances the steady escape rate. The effect of a finite number of uncoupled harmonic oscillators N on the escape dynamics of a classical open system is also discussed.

中文翻译：

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自振荡对经典和量子开放系统逃逸动力学的影响

我们通过采用系统加环境加相互作用模型研究自激振荡对经典和量子开放系统逃逸动力学的影响。对于由 Zwanzig (J. Stat. Phys. 9, 215 (1973)) 表示的具有记忆核函数的阻尼自由粒子（系统），它起源于截止频率为 wd 的德拜型谐振子浴（环境） ，发现遍历性分解是因为速度自相关函数在渐近时间的余弦函数中振荡。这种自振荡系统从亚稳态电位的稳定逃逸率表现出对 wd 的非单调依赖性，这表明存在一个最佳截止频率使其最大。比较经典和量子体制的结果，量子开放系统的稳态逃逸率降低为经典的，wd 逐渐减小，量子涨落确实提高了稳态逃逸率。还讨论了有限数量的非耦合谐振子 N 对经典开放系统的逃逸动力学的影响。