Stochastic theory of diffusion-controlled reactions

We study the kinetics of diffusion-controlled A+B→B reactions, in which both species are moving randomly on a d-dimensional lattice and react upon encounters, provided that both species are in reactive states. Particles’ reactivity fluctuates randomly between active and passive forms. We find that in low dimensions the A particle survival probability Ψ(t) is described by a stretched-exponential function of time, such that no reaction constant can be identified. In three dimensions, we recover the exponential decay law and evaluate the effective reaction constant in several particular cases. In addition, we derive some rigorous bounds on Ψ(t).