Smoothed Langevin Dynamics of Highly Oscillatory Systems

In this paper, we generalize a result by Rubin and Ungar on Hamiltonian systems with a strong constraining potential to thermally embedded systems, i.e. to Langevin dynamics. Such highly oscillatory systems arise, for example, in the context of molecular dynamics. We derive averaged equations of motion for the slowly varying solution components. This includes in particular the derivation of a correcting force-term that stands for the coupling of the slow and fast degrees of motion. We will identify two limiting cases: (i) the correcting force becomes, over a nite interval of time, almost identical to the force term suggested by Rubin and Ungar (weak thermal coupling) and (ii) the correcting force can be approximated by the gradient of the Fixman potential as used in statistical mechanics (strong thermal coupling). We also discuss smoothing in the context of constant temperature molecular dynamics.