Response to a small external force and fluctuations of a passive particle in a one-dimensional diffusive environment

Physical Review. E
François Huveneers

Abstract

We investigate the long-time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant D. We consider two cases: (a) The particle is pulled forward by a small external constant force and (b) there is no systematic bias. Theoretical arguments and numerical simulations provide evidence that the particle is eventually trapped by the environment. This is diagnosed in two ways: The asymptotic speed of the particle scales quadratically with the external force as it goes to zero, and the fluctuations scale diffusively in the unbiased environment, up to possible logarithmic corrections in both cases. Moreover, in the large D limit (homogenized regime), we find an important transient region giving rise to other, finite-size scalings, and we describe the crossover to the true asymptotic behavior.

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Citations

Sep 14, 2018·Journal of Physics. Condensed Matter : an Institute of Physics Journal·O BénichouR Voituriez
Oct 9, 2018·Physical Review Letters·Tapas Singha, Mustansir Barma

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