Abstract
In this paper we report new developments in the expansion and partial resummation of the evolution operator. Higher order resummations allow derivation of an effective one-dimensional potential which accurately represents quantum dynamics for even strongly coupled low-frequency modes. This allows a system bath approximation which can accurately reproduce multidimensional quantum mechanics. In addition the formulation presented in this paper should prove significantly easier to extend to many-body problems than previous formulations we have derived. The accuracy of the method for even highly nonadiabatic applications, and the ease of implementation suggests that this approach will be useful in the calculation of the quantum dynamics of many dimensional systems.
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