Bridging the Gap between the Ultrafast and the Ultraslow

A Brownian simulation of a microscopic pseudo-unimolecular reversible reaction in one-dimension is reported over a huge time range for varying values of the dissociation parameter. The simulation shows how the time behavior of the approach to equilibrium of the binding probability, which is predominantly power-law for ultrafast dissociation, changes to a faster decay law as dissociation slows down. In terms of the mean-field approximations which are compared with the simulations, the ultrafast dissociation limit is characterized as "superposition dominated" whereas the ulraslow limit is "convolution dominated".