Transient Superdiffusive Motion on a Disordered Ratchet Potential

Abstract

The relationship between anomalous superdiffusive behavior and particle trapping probability is analyzed on a rocking ratchet potential with spatially correlated weak disorder. The trapping probability density is shown, analytically and numerically, to have an exponential form as a function of space. The trapping processes with a low or no thermal noise are only transient, but they can last much longer than the characteristic time scale of the system and therefore might be detected experimentally. Using the result for the trapping probability we obtain an analytical expression for the number of wells where a given number of particles are trapped. We have also obtained an analytical approximation for the second-moment of the particle distribution function C2 as a function of time, when trapped particles coexist with constant velocity untrapped particles. We also use the expression for C2 to characterize the anomalous superdiffusive motion in the absence of thermal noise for the transient time.