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 generalized Langevin equation. It is found that the system exhibits two relative motion modes: the locking state and the running state. Under the surrounding of sub-Ohmic damping ($0<\delta <1$), the particle should transfer into a running state from a locking state only when local minima of the potential vanish; hence the particle occurs a synchronization oscillation in its 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 exists double centers in the velocity distribution. This induces the particle having faster diffusion, i.e., its MSD reads $<\Delta x^2(t)>=2D_{eff}^{(\delta )}{t}^{{\delta }_{eff}}$. Our result shows that the effective power index ${\delta }_{\text{eff}}$ can be enhanced and is a nonmonotonic function of the temperature and the driving force. The mixture effect of the two motion modes also leads to a breakdown of hysteresis loop of the mobility.

arXiv comment7 pages,7 figures

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