Smoothed Langevin dynamics of highly oscillatory systems
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.
scientific article; zbMATH DE number 1514733