Smoothed Langevin dynamics of highly oscillatory systems
type: Item
instance of: scholarly article
title: Smoothed Langevin dynamics of highly oscillatory systems
zbMATH Open document ID: 0953.37013
DOI: 10.1016/S0167-2789(99)00200-6
author: Sebastian Reich
published in: Physica D
publication date: 2000-10-08T00:00:00Z
review text: The author investigates normal forms of Hamiltonian systems with a strong constraining potential. The paper is related to the recent work of \textit{C. Schütte} and \textit{F. A. Bornemann} [Physica D 102, 57-77 (1997; Zbl 0896.70010)] for homogenization. The author uses recent results to estimate the truncation error of the normal form transformation of the oscillatory part in action-angle variables. On the other hand, he reduces Langevin dynamics transformed to action-angle variables by averaging. In particular, he derives a correcting force term that represents the coupling of slow and fast motion. For strong thermal coupling this appears to be close to the gradient of the Fixman potential from statistical mechanics. Furthermore, he discusses smoothing for constant temperature molecular dynamics and gives a numerical example.
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 70K70
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 92E10
Mathematics Subject Classification ID: 70H99
Mathematics Subject Classification ID: 81V55
zbMATH DE Number: 1514733
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: Langevin dynamics
zbMATH Keywords: highly oscillatory
zbMATH Keywords: smoothed dynamics
zbMATH Keywords: averaging
zbMATH Keywords: correcting potential
zbMATH Keywords: constrained system
zbMATH Keywords: molecular dynamics
zbMATH Keywords: normal form
reviewed by: Jens D. M. Rademacher
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1514733