Effect of Self-Oscillation on Escape Dynamics of Classical and Quantum Open Systems

Abstract

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.

On the Phenomenon of Low-Frequency, Large-Amplitude Oscillations in a High-Dimensional Linear Dynamical System

“…It should be noted here that the concept of self-oscillations is widely used in the modern science. For example, we refer the reader to [6][7][8][9][10][11], and for low-frequency self-oscillations, to [12].…”

Monte Carlo study of transport in low-dimensional quantum disorder systems at finite temperature

“…For instance, Barik and Ray developed the scheme employing quantum Brownian motion for multiplicative noise [29]; Bao and co-workers demonstrated that the effective coefficient of diffusion of a particle driven by quantum thermal noise in a biased periodic potential is less than the classical version when the biasing force attains its critical value obtained from the QGLE [24]. The steady escape rate of a self-oscillated system from a metastable potential exhibited in molecular dynamics simulations a nonmonotonic dependence at the cut-off frequency of a harmonic oscillator bath [30], and the magnitude and direction of the average current were affected by the nonlinear quantum dissipation in a PIMC approach [31]. Here, for finite temperatures, we shall apply the QGLE and PIMC methods mentioned above to consider the effect of disorder on the transport dynamics of a particle in the quantum domain and propose an effective classical disorder potential which is important in understanding the dynamic behavior in quantum disorder potentials.…”