2007/01/21 by Xu Cheng, X. Z. Cheng, M. B. A. Jalil +1 · 9 citations
Computer Science · Environmental Science · Mathematics · Physics and Astronomy · #Brownian motion #Brownian motor #Classical mechanics #Computer science #Current (fluid) #Ecosystem dynamics and resilience #First-hitting-time model #Langevin equation #Lévy flight #Markov chain #Mathematical analysis #Mathematics #Maxima and minima #Noise (video) #Nonlinear Dynamics and Pattern Formation #Physics #Quantum mechanics #Random walk #Ratchet #Statistical physics #Thermodynamics #Work (physics) #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physrevlett.99.070601
published in Physical Review Letters 99(7), 070601 (American Physical Society) · 4 pages, 3 figures
arxiv created 2007/01/21 · openalex publication_date 2007/08/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 current reversal in the ratchet are obtained and discussed.