Transport of particles for a spatially periodic stochastic system with correlated noises

The transport of particles for a spatially periodic stochastic system driven by two multiplicative noises and one additive noise (between which there are correlations) is investigated for the overdamped and underdamped cases. It is shown that (i) the probability current can be positive, zero, or negative; (ii) the movement of the particles represents the phenomenon of resonance as a function of the additive noise strength. For the underdamped case, the particles with different mass can be separated by controlling the system or the noise parameters. In particular, a reversal of the flux can be induced by controlling the correlations between the additive and multiplicative noises.