Noise-induced transport in a rough ratchet potential

Several years ago Zwanzig considered the diffusion in a potential that is spatially rough due to hierarchical structure of protein. We extend this idea to the overdamped Brownian dynamics in a one-dimensional periodic and rough ratchet potential. A general expression is obtained for the effective current at the steady state. Variation in both current and efficiency has been studied with respect to the amplitude of the roughness and an external nonequilibrium, nonthermal driving force. It has been shown that roughness hinders current quite significantly. Our analysis is corroborated by detailed numerical simulations and may be useful in the context of laser switching of current through molecular wire