A theory of slightly fluctuating ratchets

We consider a Brownian particle moving in a slightly fluctuating potential. Using the perturbation theory on small potential fluctuations, we derive a general analytical expression for the average particle velocity valid for both flashing and rocking ratchets with arbitrary, stochastic or deterministic, time dependence of potential energy fluctuations. The result is determined by the Green's function for diffusion in the time-independent part of the potential and by the features of correlations in the fluctuating part of the potential. The generality of the result allows describing complex ratchet systems with competing characteristic times; these systems are exemplified by the model of a Brownian photomotor with relaxation processes of finite duration.