Transport and diffusion in overdamped ratchets as a synchronization problem

The forced and overdamped motion of non-interacting particles in a periodic asymmetric potential is studied. The analysis is focused on synchronization of the motion of the particles with the external sinusoidal driving force. Two cases are considered: a perfect lattice without disorder and a lattice with non-correlated quenched noise. The amplitude of the driving force and the strength of the quenched noise are used as control parameters. The mean velocity of the particles and the diffusion coefficient are found to have a non-monotonic dependence on the quenched noise strength. These non-trivial results are explained on the basis of the synchronized motion of the individual particles in the perfect lattice.