Propagator expansions for softly coupled potentials: A model for complex reaction dynamics

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Abstract
In this paper we investigate a new approach to reduced dimensionality descriptions of quantum mechanical systems resident in a bath. We study physical situations in which the coupling between the system and the bath is slowly varying. Our method involves an operator expansion of the Feynman propagator following the Zassenhaus theorem. From this general expansion we are able to derive an especially simple special case in which the coupling is a slowly varying function of the position operators of the system and the bath. From the approximate propagator after tracing over bath degrees, we are able to derive a short time propagator which yields both a form for efficient numerical calculation and an effective Schrödinger equation for the evolution of the system under the average influence of the bath. This theory is then applied to tunneling rearrangement in mixed crystals of benzoic acid. We find that independent of potential energy perturbations, dynamic system bath couplings increase the rate of tunneling. A central goal of this type of approach is to model the increasingly complex experimental data for large (often biological) systems.