Dispersive anomalous diffusive transport in ratchets with long-range correlated spatial disorder

The effects of quenched disorder with long-range spatial correlations on the transport properties of an overdamped periodic ratchet are investigated. The modified Fourier-filtering method is applied to generate the long-range correlated spatial disorder with statistical properties [Formula presented] where [Formula presented] is the correlation exponent. Small amounts of this kind of quenched disorder are introduced in the equation of overdamped motion of a continuous time system, and the first two moments [Formula presented] and [Formula presented] are calculated. We show that the drift velocity is almost independent of [Formula presented] However, as a consequence of the long-range spatial correlations, the dispersive anomalous diffusve motion [Formula presented] appears in ratchets, with the difussion exponent H [Formula presented] being dependent on [Formula presented] Moreover, we show that both the amount of quenched disorder and the correlation degree can enhance the anomalous diffusive transport.