Weak directed transport of inertial Lévy flights in rough corrugated potential

Abstract

The directed transport of inertial Lévy flights resulting from the superimposed roughness in a corrugated potential is investigated in this paper. The influence of the roughness on the transport is studied by calculating the mean velocity (MV) and the mean first escape time (MFET), with respect to the Lévy index [Formula: see text] and the asymmetry parameter [Formula: see text] which determines the asymmetry of the potential. The results indicate that the particles’ directed transport caused by the asymmetry of the potential will be counteracted by the roughness, which behaves as the absolute value of the MV decreases with roughness [Formula: see text] increasing, and the MFET increases with [Formula: see text] increasing, correspondingly. Though smaller Lévy index [Formula: see text] can produce more large jumps, which yield the enhancement of the directed transport, since the roughness superimposed on the corrugated potential supplies the hinder effect, the directed transport is also weakened after the appearance of the roughness.