Homogenization for Generalized Langevin Equations with Applications to Anomalous Diffusion

Soon Hoe Lim, Jan Wehr, Maciej Lewenstein

Research output: Contribution to journalArticle

Abstract

We study homogenization for a class of generalized Langevin equations (GLEs) with state-dependent coefficients and exhibiting multiple time scales. In addition to the small mass limit, we focus on homogenization limits, which involve taking to zero the inertial time scale and, possibly, some of the memory time scales and noise correlation time scales. The latter are meaningful limits for a class of GLEs modeling anomalous diffusion. We find that, in general, the limiting stochastic differential equations for the slow degrees of freedom contain non-trivial drift correction terms and are driven by non-Markov noise processes. These results follow from a general homogenization theorem stated and proven here. We illustrate them using stochastic models of particle diffusion.

Original languageEnglish (US)
Pages (from-to)1813-1871
Number of pages59
JournalAnnales Henri Poincare
Volume21
Issue number6
DOIs
StatePublished - Jun 1 2020

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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