Current reversals in ratchets driven by trichotomous noise

The colored three-level Markovian noise-driven nonequilibrium dynamics of o verdamped Brownian particles in a spatially periodic asymmetric potential ( ratchet) is investigated. An explicit second-order linear ordinary differen tial equation for the stationary probability density distribution is obtain ed for the process. In the case of a piecewise linear potential with an add itive three-level (trichotomous) noise the exact formula for the stationary current is presented. The dependence of the current reversals on the noise parameters is investigated in detail and illustrated by a phase diagram. A symptotic formulas for the current for various limits of the noise paramete rs are found and compared with the results of other authors. Applications t o the fluctuation-induced separation of particles are also discussed.