An analytical study of the Berezhkovskii-Pollak-Zitserman theory of rate processes in the memory-suppression region Original Research Article

We study analytically the improved canonical variational transition state theory of rate processes recently introduced by Berezhkovskii, Pollak and Zitserman for a quartic potential added to a parabolic barrier and for a memory friction kernel having an infinite relaxation time. A hallmark of this theory is the use of the most general planar surface dividing the reactants and the products in order to optimize the rate. The optimized rate thus obtained is generally less than that given by the Grote-Hynes theory. The biggest decrease occurs in the so-called memory suppression region, where the memory relaxation time is very long. The behavior of the rate is conveniently analyzed in terms of a “nonlinearity parameter” χ. We find that the most interesting effects take place when χ gets “stuck” at zero. This is exactly analogous to an ideal Bose gas, in which the chemical potential gets “stuck” at zero below its critical temperature. This analogy turns out to be very useful in studying the model. We calculate the rate in different regimes and show that it obeys a scaling relation. We then study the scaling function to reveal interesting effects associated with the finiteness of the barrier height.