Mean first passage time approach to the problem of optimal barrier subdivision for Kramer's escape rate

Abstract

We consider the effect of subdividing the potential barrier along the reaction coordinate on Kramer's escape rate for a model potential. Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate. We cast the problem as a mean first passage time problem of a biased random walker and obtain equivalent results. We briefly summarize the results of our investigation on the increase in the escape rate by placing a blow-torch in the unstable part of one of the potential wells.