Saltatory drift in a randomly driven two-wave potential

TL;DR

This paper investigates how a particle in a two-wave, randomly driven potential can exhibit a saltatory unidirectional drift due to fluctuation-induced locking points, even when the average external force is zero.

Contribution

It introduces a novel mechanism explaining saltatory drift in a two-wave potential driven by random forces, supported by analytical and numerical analysis.

Findings

Particle can drift unidirectionally against average force

Saltatory drift persists even with zero average external force

Analytical estimates for terminal velocity are provided

Abstract

Dynamics of a classical particle in a one-dimensional, randomly driven potential is analysed both analytically and numerically. The potential considered here is composed of two identical spatially-periodic saw-tooth-like components, one of which is externally driven by a random force. We show that under certain conditions the particle may travel against the averaged external force performing a saltatory unidirectional drift with a constant velocity. Such a behavior persists also in situations when the external force averages out to zero. We demonstrate that the physics behind this phenomenon stems from a particular behavior of fluctuations in random force: upon reaching a certain level, random fluctuations exercise a locking function creating points of irreversibility which the particle can not overpass. Repeated (randomly) in each cycle, this results in a saltatory unidirectional drift. This mechanism resembles the work of an escapement-type device in watches. Considering the overdamped limit, we propose simple analytical estimates for the particle's terminal velocity.