Molecular motor with a build-in escapement device

G. Oshanin; J. Klafter; M. Urbakh

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arXiv · cond-mat/0312488

Molecular motor with a build-in escapement device

G. Oshanin·J. Klafter·M. Urbakh

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Abstract

We study dynamics of a classical particle in a one-dimensional potential, which is composed of two periodic components, that are time-independent, have equal amplitudes and periodicities. One of them is externally driven by a random force and thus performs a diffusive-type motion with respect to the other. We demonstrate that here, under certain conditions, the particle may move unidirectionally with a constant velocity, despite the fact that the random force averages out to zero. We show that the physical mechanism underlying such a phenomenon resembles the work of an escapement-type device in watches; upon reaching certain level, random fluctuations exercise a locking function creating the points of irreversibility in particle's trajectories such that the particle gets uncompensated displacements. Repeated (randomly) in each cycle, this process ultimately results in a random ballistic-type motion. In the overdamped limit, we work out simple analytical estimates for the particle's terminal velocity. Our analytical results are in a very good agreement with the Monte Carlo data.

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G. Oshanin, J. Klafter, M. Urbakh. 2003-12-18. Molecular motor with a build-in escapement device. https://arxiv.org/abs/cond-mat/0312488

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