Homogenization for a Class of Generalized Langevin Equations with an Application to Thermophoresis
Mathematical Physics
2020-12-16 v2 math.MP
Probability
Abstract
We study a class of systems whose dynamics are described by generalized Langevin equations with state-dependent coefficients. We find that in the limit, in which all the characteristic time scales vanish at the same rate, the position variable of the system converges to a homogenized process, described by an equation containing additional drift terms induced by the noise. The convergence results are obtained using the main result in \cite{hottovy2015smoluchowski}, whose version is proven here under a weaker spectral assumption on the damping matrix. We apply our results to study thermophoresis of a Brownian particle in a non-equilibrium heat bath.
Keywords
Cite
@article{arxiv.1704.00134,
title = {Homogenization for a Class of Generalized Langevin Equations with an Application to Thermophoresis},
author = {Soon Hoe Lim and Jan Wehr},
journal= {arXiv preprint arXiv:1704.00134},
year = {2020}
}
Comments
The contents and results of the paper have been revised and corrected from a previous version