Dichotomic ratchet in a two-dimensional corrugated channel
We consider a particle diffusing in a two-dimensional (2D) channel of varying width h(x). It is driven by a force of constant magnitude f but random orientation there or back along the channel. We derive the effective generalized Fick-Jacobs equation for this system, which describes the dynamics of...
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| Published in | Physical review. E Vol. 104; no. 6-1; p. 064115 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
United States
01.12.2021
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| Online Access | Get more information |
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| Summary: | We consider a particle diffusing in a two-dimensional (2D) channel of varying width h(x). It is driven by a force of constant magnitude f but random orientation there or back along the channel. We derive the effective generalized Fick-Jacobs equation for this system, which describes the dynamics of such a particle in the longitudinal coordinate x. Aside from the effective diffusion coefficient D(x), our mapping also generates an additional effective potential -γ(x) added to the entropic potential -log[h(x)]. It acquires an increasing or decreasing component in asymmetric periodic channels, and thus it explains appearance of the ratchet current. We study this effect on a trial example and compare the results of our true 2D theory with a commonly used effective one-dimensional description; the data are verified by the numerical solution of the full 2D problem. |
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| ISSN: | 2470-0053 |
| DOI: | 10.1103/PhysRevE.104.064115 |