Classical dynamics of a coupled double well oscillator in condensed mediaa)

Abstract

The influence of a deterministic coupling between the reaction coordinate and a transverse normal mode on the reaction rate is considered within the context of classical (stochastic) dynamics. Our theoretical approach is based on a scheme of elimination of rapidly relaxing (irrelevant) variables. This procedure, perturbational in nature, makes it possible to get corrections of increasing accuracy to the results of the ‘‘standard adiabatic method’’ as perturbation terms of higher and higher order are taken into account. In the large friction case, the very first significant correction to the standard adiabatic scheme is shown to picture the reaction coordinate as being driven by a diffusionlike equation exhibiting instability phenomena. Thus, our approach makes an intriguing link between the activation of a reaction process via excitation of a nonreactive normal mode and noise-induced phase transition phenomena. When the frequency of the nonreactive mode varies slowly with the reaction coordinate, the reaction threshold can be expressed by a simple analytical formula. Results of computer calculations, which allow the exploration of a still wider range of physical conditions, are also discussed.