Escape times and diffusion coefficients in fluctuating potentials

摘要

We investigate an overdamped Brownian particle moving in: a) a dichotomously fluctuating metastable potential; b) a fast fluctuating periodic potential. For piece-wise linear potential we obtain for case (a) the exact mean first-passage time as a function of the potential parameters, the noise intensity and the mean frequency of switchings of the dichotomous noise. We find noise enhanced stability (NES) in the system investigated. The parameter regions of the fluctuating potential where NES effect can be observed are analytically derived. For case (b) we consider a symmetric periodic potential modulated by white noise. We obtain for such a potential the same relationship between effective diffusion coefficient of Brownian particles and the mean first-passage time, discovered previously for fixed periodic potential. The phenomenon of diffusion acceleration in comparison with free particle case has been found for arbitrary potential profile. The effective diffusion coefficients for sawtooth, sinusoidal and piece-wise parabolic potentials are calculated in closed analytical form.