Scaling limits for the generalized langevin equation
File(s)PavliotisStoltzVaes2021.pdf (751.34 KB)
Accepted version
Author(s)
Pavliotis, GA
Stoltz, G
Vaes, U
Type
Journal Article
Abstract
In this paper, we study the diffusive limit of solutions to the generalized Langevin equation (GLE) in a periodic potential. Under the assumption of quasi-Markovianity, we obtain sharp longtime equilibration estimates for the GLE using techniques from the theory of hypocoercivity. We then show asymptotic results for the effective diffusion coefficient in the small correlation time regime, as well as in the overdamped and underdamped limits. Finally, we employ a recently developed numerical method (Roussel and Stoltz in ESAIM Math Model Numer Anal 52(3):1051–1083, 2018) to calculate the effective diffusion coefficient for a wide range of (effective) friction coefficients, confirming our asymptotic results.
Date Issued
2021-02
Date Acceptance
2020-11-29
Citation
Journal of Nonlinear Science, 2021, 31 (1), pp.1-58
ISSN
0938-8974
Publisher
Springer Science and Business Media LLC
Start Page
1
End Page
58
Journal / Book Title
Journal of Nonlinear Science
Volume
31
Issue
1
Copyright Statement
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021. The final publication is available at Springer via https://doi.org/10.1007/s00332-020-09671-4
Sponsor
Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Identifier
https://link.springer.com/article/10.1007%2Fs00332-020-09671-4#Abs1
Grant Number
EP/P031587/1
VP1-2019-019
Subjects
math-ph
math-ph
cond-mat.stat-mech
math.MP
35B40, 46N30, 35Q84, 82M22, 60H10
0102 Applied Mathematics
Fluids & Plasmas
Publication Status
Published
Article Number
8
Date Publish Online
2021-01-02