Roughness-enhanced transport in a tilted ratchet driven by Lévy noise

The enhanced transport of particles by roughness in a tilted rough ratchet potential subject to a Lévy noise is investigated in this paper. Due to the roughness, the transport process exhibits quite different properties compared to the smooth case. We find that the roughness on the potential wall functions like a ladder to provide the convenience for particles to climb up but hinder them to slide down. The mean first passage time from one well to its right adjacent well and the mean velocity are, respectively, calculated versus the roughness, the external force, and the Lévy stability index. Our results show that the roughness is able to induce an enhancement on the mean velocity of particles and accelerate the barrier crossing process. The general conditions require a small external force and a small Lévy stability index. We find that with increasing external forces, the enhancement areas of roughness and Lévy stability index both shrink. However, for the Lévy stability index within the enhancement area, its increase will enlarge the enhancement area of roughness. On the contrary, under the same conditions we observe that for a Gaussian noise the roughness always reduces the corresponding mean velocity which is very different from the case of Lévy noise.