Energy diffusion in many-dimensional Markovian systems: The consequences of competition between inter- and intramolecular vibrational energy transfer

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Abstract
We examine the dynamics of barrier crossing using a two-dimensional Langevin equation in the low friction regime. We find that as the friction on the nonreactive mode is increased there is a transition from two-dimensional Markovian dynamics to one-dimensional non-Markovian dynamics resulting in a qualitative change in the behavior of the rate constant as a function of friction. This result supports the conclusion that existing theories which predict rates for energy activation in Markovian and non-Markovian systems have limited ranges of validity and are not as general as had previously been supposed. A method is proposed which analyzes the eigenvalues of the full system and provides a criterion for the validity of the various theories. These ideas are then used to interpret the results of a recent experimental study. In the Appendix we discuss, in some detail, the role of a random force in aiding intramolecular energy transfer.