Bistability effects of the brownian motion in periodic potentials

Abstract

In the stationary state the equation of motion for particles moving in a periodic potential has two solutions, a locked one and a running one, for low and intermediate damping constants and for suitable external forces. The effect of an additional Langevin force to this bistable behaviour is investigated. For finite noise strength, the mobility depends continuously on the external force, whereas in the limit of vanishing strength of the noise force one gets a sharp transition between the locked and the running solution at a critical external force. This critical force is calculated exactly in the low friction limit and approximately for intermediate friction constants. Furthermore the temperature dependence for various forces including the critical one is shown in the low friction limit.