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A "Burnt Bridge'' Brownian Ratchet

T. Antal·P. L. Krapivsky
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Abstract

Motivated by a biased diffusion of molecular motors with the bias dependent on the state of the substrate, we investigate a random walk on a one-dimensional lattice that contains weak links (called "bridges'') which are affected by the walker. Namely, a bridge is destroyed with probability p when the walker crosses it; the walker is not allowed to cross it again and this leads to a directed motion. The velocity of the walker is determined analytically for equidistant bridges. The special case of p=1 is more tractable -- both the velocity and the diffusion constant are calculated for uncorrelated locations of bridges, including periodic and random distributions.

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BibTeXRIS

T. Antal, P. L. Krapivsky. 2005-04-26. A "Burnt Bridge'' Brownian Ratchet. https://doi.org/10.1103/physreve.72.046104

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