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Evolution of a passive particle in a one-dimensional diffusive environment

Huveneers, François; Simenhaus, François (2020), Evolution of a passive particle in a one-dimensional diffusive environment. https://basepub.dauphine.psl.eu/handle/123456789/22109

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-03071641
Date
2020
Series title
Cahier de recherche du CEREMADE
Pages
27
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Author(s)
Huveneers, François
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Simenhaus, François
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We study the behavior of a tracer particle driven by a one-dimensional fluctuating potential, defined initially as a Brownian motion, and evolving in time according to the heat equation. We obtain two main results. First, in the short time limit, we show that the fluctuations of the particle become Gaussian and sub-diffusive, with dynamical exponent 3/4. Second, in the long time limit, we show that the particle is trapped by the local minima of the potential and evolves diffusively i.e. with exponent 1/2.
Subjects / Keywords
particule