An analytical study of the Berezhkovskii-Pollak-Zitserman theory of rate processes in the critical region. II. The critical coupling plane Original Research Article

In a recent paper, we studied analytically the canonical variational transition state theory of rate processes, introduced by Berezhkovskii, Pollak and Zitserman (BPZ). We used a quartic potential added to a parabolic barrier and a memory friction kernel having an infinite relaxation time. We found that their memory suppression region, where the rate can deviate significantly from the Grote-Hynes (GH) theory, is identical to the critical region. We showed that the BPZ rate obeys a scaling relation in this region and studied the scaling function in different coupling regimes. The most important result of this work was to show the existence of a critical line of singularities in the infinite relaxation time plane. In this paper, we extend the results to a finite relaxation time and obtain a more general scaling function. We then study this scaling function near the GH limit in order to ascertain the deviations of the BPZ rate from the GH theory due to the finiteness of the barrier height. We also study the behavior of the rate in the critical coupling plane and show that in this plane too, there is a line of critical points where the behavior of the rate is singular and changes dramatically as this line is crossed.