Steady-state diffusion-controlled A+B→0 reactions in two and three dimensions: Rate laws and particle distributions

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Abstract
In this article we study the elementary diffusion-limited reaction A+B→0, for a system of particles with hard-core interactions. We extend a theoretical investigation carried out for dimension d=1 to higher Euclidean dimensions. We show that a source or a first-order decay mechanism can control the steady-state distribution of particles. We derive in dimensions d=2 and 3 the explicit correlation functions and macroscopic reaction laws. We calculate a segregation length, measuring the extent of the clustering for particles of the same type, and we derive its dependence on the Euclidean dimension, the detailed source term structure, and a possible internal decay mechanism.