Projected dynamics: Analysis of a chemical reaction model

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Abstract
The rate processes corresponding to barrier crossing dynamics in a symmetric double-well potential driven by a white-noise source are investigated. The rate kernels in the generalized phenomenological rate law describing the reaction involve time evolution through a projected Fokker–Planck operator. The spectral properties of the projected Fokker–Planck operator are studied, and the rate kernels are expressed in terms of the eigenvalues and eigenfunctions of this operator. The formal results are illustrated with numerical calculations. The results provide information on the nature of the generalized chemical rate law for fast processes.