Open Access

Sebastian Reich

• In this paper we generalize a result by Rubin and Ungar on Hamiltonian systems containing a strong constraining potential to Langevin dynamics. Such highly oscillatory systems arise, for example, in the context of molecular dynamics. We derive constrained 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 finite 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). The discussion will shed some light on the question which of the two correcting potentials is more appropriate under which circumstances for molecular dynamics. In Sec.~7, we also discuss smoothing in the context of constant temperature molecular dynamics.