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

TL;DR

This study explores how non-Ohmic damping influences particle transport in a tilted periodic potential, revealing distinct motion modes, their coexistence, and effects on diffusion and hysteresis through Monte Carlo simulations.

Contribution

It introduces a detailed analysis of state transitions and coexistence of motion modes in non-Ohmic damping systems, highlighting nonmonotonic behavior of effective diffusion parameters.

Findings

Locking and running states depend on potential minima

Coexistence of motion modes occurs in super-Ohmic damping

Effective diffusion index varies nonmonotonically with temperature and force

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 $<\Delta x^2(t)> = 2D^{(\delta)}_{eff} t^{\delta_{eff}}$. Our result shows that the effective power index $\delta_{\textmd{eff}}$ 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.