Minimal Brownian Ratchet: An Exactly Solvable Model

Details Minimal Brownian Ratchet: An Exactly Solvable Model Minimal Brownian Ratchet: An Exactly Solvable Model

2002-05-15

arxiv.org/abs/cond-mat/0205302v2

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures, RevTex source, General solution added. To be appeared in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.91.220601

We develop an exactly-solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations we obtain the steady-state probabilities. Generally the steady-state solution does not display detailed balance, giving rise to an induced directional motion in the MBR. For a reduced two-dimensional parameter space we find the null-curve on which the net current vanishes and detailed balance holds. A system on this curve is said to be balanced. On the null-curve, an additional source of external random noise is introduced to show that a directional motion can be induced under the zero overall driving force. We also indicate the off-balance behavior with biased random noise.

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