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

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Date
2018
Dewey
Probabilités et mathématiques appliquées
Sujet
force; fluctuations; one-dimensional diffusive environment
Journal issue
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Volume
97
Number
4-1
Publication date
04-2018
Publisher
American Physical Society
DOI
http://dx.doi.org/10.1103/PhysRevE.97.042116
URI
https://basepub.dauphine.fr/handle/123456789/18702
Collections
  • CEREMADE : Publications
Metadata
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Author
Huveneers, François
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
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.

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