Transport in randomly-fluctuating spatially-periodic potentials

The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical simulations show two distinct parameter regimes, corresponding to free-running near-deterministic particles, and particles which are trapped in local minima of the potential with intermittent escape flights. Perturbation and asymptotic methods are developed to understand the drift velocity and diffusion coefficient in each parameter regime.