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 eta(x)eta(x('))similar to\x(')-x\(-gamma), where gamma 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 C-1(t)=<x(t)> and C-2(t)=<(x(t)-<x(t)>)(2)> are calculated. We show that the drift velocity is almost independent of gamma. However, as a consequence of the long-range spatial correlations, the dispersive anomalous diffusve motion [C-2(t)similar tot(H)] appears in ratchets, with the difussion exponent H (1<H<2) being dependent on gamma. Moreover, we show that both the amount of quenched disorder and the correlation degree can enhance the anomalous diffusive transport.