Molecular motor with a built-in escapement device

¹ Laboratoire de Physique Théorique des Liquides, Université Paris 6, Tour 16 4 place Jussieu, 75252 Paris Cedex 05, France
² Max-Planck-Institut für Metallforschung - Heisenbergstr. 3 D-70569 Stuttgart, Germany and Institut für Theoretische und Angewandte Physik, Universität Stuttgart Pfaffenwaldring 57, D-70569 Stuttgart, Germany
³ School of Chemistry, Tel Aviv University - 69978 Tel Aviv, Israel

Received: 19 December 2003
Accepted: 3 August 2004

Abstract

We study the dynamics of a classical particle in a one-dimensional potential composed of two identical spatially periodic components, one of which is externally driven by a random force. We demonstrate that, under certain conditions, the particle may move unidirectionally with a constant velocity, despite the fact that the average external force is zero. We show that the physical mechanism underlying such a phenomenon resembles the work of an escapement-type device in watches; upon reaching a certain level, random fluctuations exercise a locking function creating points of irreversibility which the particle cannot overpass. Repeated (randomly) in each cycle, this results in a saltatory 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 Monte Carlo results.