State transition of a non-Ohmic damping system in a corrugated plane

Abstract

Anomalous transport of a particle subjected to non-Ohmic damping of the power delta in a tilted periodic potential is investigated via Monte Carlo simulation of the generalized Langevin equation. It is found that the system exhibits two relative motion modes: the locked state and the running state. In an environment of sub-Ohmic damping (0<delta<1) , the particle should transfer into a running state from a locked state only when local minima of the potential vanish; hence a synchronization oscillation occurs in the particle's mean displacement and mean square displacement (MSD). In particular, the two motion modes are allowed to coexist in the case of super-Ohmic damping (1<delta<2) for moderate driving forces, namely, where double centers exist in the velocity distribution. This causes the particle to have faster diffusion, i.e., its MSD reads <Deltax(2)(t)>=2D_(eff)(delta){t(delta_eff} . Our result shows that the effective power index delta_(eff) can be enhanced and is a nonmonotonic function of the temperature and the driving force. The mixture of the two motion modes also leads to a breakdown of the hysteresis loop of the mobility.