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Saltatory drift in a randomly driven two-wave potential

G. Oshanin·J. Klafter·M. Urbakh
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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.

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G. Oshanin, J. Klafter, M. Urbakh. 2005-10-17. Saltatory drift in a randomly driven two-wave potential. https://doi.org/10.1088/0953-8984%2F17%2F47%2F004

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