Anomalous transport in unbound and ratchet potentials.

Abstract

A non-Markovian Langevin equation with a broadband noise is proposed to describe anomalous transport of a particle passing over a potential saddle or moving in a ratchet potential. In the presence of thermal broadband noise, the asymptotic mean square displacement of a free particle is proportional to the square of time; this is called ballistic diffusion. The passing probability of a particle driven by this broadband noise over the saddle of an inverted harmonic potential is obtained analytically. It is shown that the passing probability increases with the kinetic energy, which is slower than that of normal case. The mechanisms of ballistic diffusion and mobility are also applied to the rocking (a square-wave driving force acting on the potential) and flashing (the potential fluctuating between on and off) ratchets. Phenomena such as acceleration and double-peak mean velocity are observed.