Spatial structure in diffusion-limited two-species annihilation

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Abstract
We report on the spatial distribution of particles in the reaction A+B→0. For the spatial dimension d≤4, this process exhibits anomalously slow kinetics which stems from the formation of a mosaic of continuously growing domains which contain only one of the two species. We investigate the temporal evolution of the distribution of domain sizes, as well as the distribution of interparticle distances between closest-neighbor particles, both between the same and opposite species. Our results are considerably richer than might at first be expected. The average distance between closest-neighbor AB pairs scales differently than the corresponding distance between same-species pairs. The full distribution of AA separations is found to reflect the competing influences of these two length scales. Many of our observations can be accounted for in terms of simple scaling arguments. Rather surprisingly, many of our results are drastically altered if one of the species is immobile. The spatial distribution of the immobile reactant exhibits a self-similar character, leading to complex behavior for the moments of the interparticle distance distribution.