Response to a small external force and fluctuations of a passive particle in a one-dimensional diffusive environment
Huveneers, François (2018), Response to a small external force and fluctuations of a passive particle in a one-dimensional diffusive environment, Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 97, 4-1. 10.1103/PhysRevE.97.042116
TypeArticle accepté pour publication ou publié
Journal namePhysical Review. E, Statistical, Nonlinear, and Soft Matter Physics
American Physical Society
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)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.
Subjects / Keywordsforce; fluctuations; one-dimensional diffusive environment
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