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From ballistic to diffusive behavior in periodic potentials
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Hairer, Martin and Pavliotis, G. A. (2008) From ballistic to diffusive behavior in periodic potentials. Journal of Statistical Physics, Vol.131 (No.1). pp. 175-202. doi:10.1007/s10955-008-9493-3 ISSN 0022-4715.
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Official URL: http://dx.doi.org/10.1007/s10955-008-9493-3
Abstract
The long-time/large-scale, small-friction asymptotic for the one dimensional Langevin equation with a periodic potential is studied in this paper. It is shown that the Freidlin-Wentzell and central limit theorem (homogenization) limits commute. We prove that, in the combined small friction, long-time/large-scale limit the particle position converges weakly to a Brownian motion with a singular diffusion coefficient which we compute explicitly. We show that the same result is valid for a whole one parameter family of space/time rescalings. The proofs of our main results are based on some novel estimates on the resolvent of a hypoelliptic operator.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Homogenization (Differential equations), Hypoelliptic operators, Periodic functions, Perturbation (Mathematics), Langevin equations | ||||
Journal or Publication Title: | Journal of Statistical Physics | ||||
Publisher: | Springer New York LLC | ||||
ISSN: | 0022-4715 | ||||
Official Date: | April 2008 | ||||
Dates: |
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Volume: | Vol.131 | ||||
Number: | No.1 | ||||
Number of Pages: | 28 | ||||
Page Range: | pp. 175-202 | ||||
DOI: | 10.1007/s10955-008-9493-3 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Data sourced from Thomson Reuters' Web of Knowledge
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