| Summary: | 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 <inline-formula><math display="inline"><semantics><msub><mi>w</mi><mi>d</mi></msub></semantics></math></inline-formula>, 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 <inline-formula><math display="inline"><semantics><msub><mi>w</mi><mi>d</mi></msub></semantics></math></inline-formula>, 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 <inline-formula><math display="inline"><semantics><msub><mi>w</mi><mi>d</mi></msub></semantics></math></inline-formula> decreasing gradually, and quantum fluctuation indeed enhances the steady escape rate. The effect of a finite number of uncoupled harmonic oscillators <i>N</i> on the escape dynamics of a classical open system is also discussed.
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