Exactly solvable model of a slightly fluctuating ratchet

We consider the motion of a Brownian particle in sawtooth potential dichotomously modulated by spatially harmonic perturbation. An explicit expression for Laplace transform Green function an extremely asymmetric is obtained. With this result, within approximation small potential-energy fluctuations, integration relations average velocity performed elementary terms. The obtained analytical its high-temperature, low-frequency, and high-frequency asymptotics, as well numerical calculations arbitrary symmetry, indicate that such system, frequency-temperature controlling magnitude direction ratchet becomes possible. clarify mechanism appearance additional regions nonmonotonicity frequency dependence velocity, which leads to stopping points. This consequence competition between sliding time along steep slope highly correlation dichotomous noise.