Escape times in fluctuating metastable potential and acceleration of diffusion in periodic fluctuating potentials

The problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered. For the overdamped Brownian particle moving in a piecewise linear dichotomously fluctuating metastable potential, we obtain the mean first-passage time as a function of the potential parameters, the noise intensity and the mean rate of switchings of the dichotomous noise. We find noise-enhanced stability phenomenon in the system investigated and the parameter region of the fluctuating potential where the effect can be observed. For the diffusion of the overdamped Brownian particle in a fast fluctuating symmetric periodic potential we obtain that the effective diffusion coefficient depends on the mean first-passage time, as discovered for fixed periodic potential. The effective diffusion coefficients for sawtooth, sinusoidal and piecewise parabolic potentials are calculated in closed analytical form.