Non-Markovian dynamics and barrier crossing rates at high viscosity

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Abstract
Using the formulation developed in the preceding paper we explain the anomalous simulation results of Straub, Borkovec, and Berne for barrier crossing rates in a double well potential. We find that even in the high friction regime the well dynamics may have a significant effect on rate constants. By using model potentials and memory kernels we show that the dynamics can resemble not only spatial diffusion but also energy diffusion. This is due to the viscoelastic nature of a non-Markovian interaction with a bath. In general, the well dynamics is a complicated mixture of energy and spatial diffusion processes. We find analytical expressions for rate constants valid when the well dynamics is near or far from the Markovian limit.