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Journal Articles Journal of Nonlinear Science Year : 2021

Scaling limits for the generalized Langevin equation


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.

Dates and versions

hal-02911852 , version 1 (04-08-2020)



Grigorios A. Pavliotis, Gabriel Stoltz, Urbain Vaes. Scaling limits for the generalized Langevin equation. Journal of Nonlinear Science, 2021, 31, pp.8. ⟨10.1007/s00332-020-09671-4⟩. ⟨hal-02911852⟩
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