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arXiv · 2007.16087

Scaling limits for the generalized Langevin equation

G. A. Pavliotis·G. Stoltz·U. Vaes
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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 prove asymptotic results for the effective diffusion coefficient in three limiting regimes: the short memory, the overdamped and the underdamped limits. Finally, we employ a recently developed spectral numerical method in order to calculate the effective diffusion coefficient for a wide range of (effective) friction coefficients, confirming our asymptotic results.

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BibTeXRIS

G. A. Pavliotis, G. Stoltz, U. Vaes. 2020-11-20. Scaling limits for the generalized Langevin equation. https://doi.org/10.1007/s00332-020-09671-4

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