Analytical Solution to Transport in Brownian Ratchets via Gambler's Ruin Model

Details Analytical Solution to Transport in Brownian Ratchets via Gambler's Ruin Model Analytical Solution to Transport in Brownian Ratchets via Gambler's Ruin Model

2007-01-21

arxiv.org/abs/cond-mat/0701505v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.99.070601

We present an analogy between the classic Gambler's Ruin problem and the thermally-activated dynamics in periodic Brownian ratchets. By considering each periodic unit of the ratchet as a site chain, we calculated the transition probabilities and mean first passage time for transitions between energy minima of adjacent units. We consider the specific case of Brownian ratchets driven by Markov dichotomous noise. The explicit solution for the current is derived for any arbitrary temperature, and is verified numerically by Langevin simulations. The conditions for vanishing current and current reversal in the ratchet are obtained and discussed.

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