Stochastic resonance, Brownian ratchets and the Fokker-Planck Equation

Abstract

Our immediate aim is to arrive at quantitative realistic estimates of the optimum noise levels for a complete and feasible Brownian ratchet device. A number of difficult "Unsolved Problems of Noise"naturally arise in the course of this work. We pose a general philosophical question: "Is it is possible to relate stochastic resonance and Brownian ratchets in a formal way, through a consideration of the Fokker-Planck equation?"The evidence suggests that some forms of stochastic resonance can be formulated in terms of a Fokker-Planck equation and some cannot. Stochastic resonance may actually be a collection of similar but distinct phenomena. We present a number of simulations which demonstrate stochastic resonance in a Brownian ratchet. We also show how current is dependent on a number of other parameters.