A THEORY FOR THE ACTIVATED BARRIER CROSSING RATE-CONSTANT IN SYSTEMS INFLUENCED BY SPACE AND TIME-DEPENDENT FRICTION

A general theory is presented for the thermally activated rate constan t in systems influenced by spatially dependent and. time correlated fr iction. The theory is valid at all damping strengths and goes uniforml y from the energy diffusion limit to the spatial diffusion limit. Resu lts of the theory for a model system with an exponentially time correl ated and spatially dependent friction kernel are compared with results from a numerically exact solution of the equivalent generalized Lange vin equation. Predictions of the theory are found to be in excellent a greement with the numerical simulation results. The phenomenon of memo ry suppression of the rate is observed for long time scale frictions a nd its modification due to the spatial dependence of the friction is d iscussed. The effects of spatially dependent friction can be understoo d through a quantity called the ''average spatial modification'' of th e coupling between the reaction coordinate and the environment.