On mathematical foundation of the Brownian motor theory
Mathematical Physics
2020-03-09 v2 Analysis of PDEs
math.MP
Abstract
The paper contains mathematical justification of basic facts concerning the Brownian motor theory. The homogenization theorems are proved for the Brownian motion in periodic tubes with a constant drift. The study is based on an application of the Bloch decomposition. The effective drift and effective diffusivity are expressed in terms of the principal eigenvalue of the Bloch spectral problem on the cell of periodicity as well as in terms of the harmonic coordinate and the density of the invariant measure. We apply the formulas for the effective parameters to study the motion in periodic tubes with nearly separated dead zones.
Keywords
Cite
@article{arxiv.1304.6790,
title = {On mathematical foundation of the Brownian motor theory},
author = {L. Koralov and S. Molchanov and B. Vainberg},
journal= {arXiv preprint arXiv:1304.6790},
year = {2020}
}
Comments
A mistake in the statement of Theorem 2.5 was corrected