Homogenization for Generalized Langevin Equations with Applications to Anomalous Diffusion

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...

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Bibliographic Details
Published inAnnales Henri Poincaré Vol. 21; no. 6; pp. 1813 - 1871
Main Authors Lim, Soon Hoe, Wehr, Jan, Lewenstein, Maciej
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2020
Springer Nature B.V
Subjects
Classical and Quantum Gravitation
Differential equations
Dynamical Systems and Ergodic Theory
Elementary Particles
Homogenization
Mathematical and Computational Physics
Mathematical Methods in Physics
Particle diffusion
Physics
Physics and Astronomy
Primary 60H10
Quantum Field Theory
Quantum Physics
Relativity Theory
Secondary 82C31
Stochastic models
Theoretical
Time
Secondary 82C31
Primary 60H10
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Summary: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.
ISSN:1424-0637
1424-0661
1424-0661
DOI:10.1007/s00023-020-00889-2