Non-Stationary and Resonant Passage of a System: A High-Frequency Cutoff Noise

Abstract

We study non-equilibrium behaviors of a particle subjected to a high-frequency cutoff noise in terms of generalized Langevin equation, where the spectrum of internal noise is considered to be of the generalized Debye form. A closed solution is impossible even if the equation is linear, because the Laplace transform of the memory kernel is a multi-value function. We use a numerical method to calculate the velocity correlation function of a force-free particle and the probability of a particle passing over the top of an inverse harmonic potential. We indicate the nonergodicity of the second type, i.e., the auto-correlation function of the velocity approaches to non-stationary at large times. Applied to the barrier passage problem, we find and analyse a resonant phenomenon that the dependence of the cutoff frequency is nonmonotonic when the initial directional velocity of the particle is less than the critical value, the latter is determined by the passing probability equal to 0.5.