Inter-Particle Distribution Functions for One-Species Diffusion-Limited Annihilation, A+A->0

Abstract

Diffusion-limited annihilation, $A+A\to 0$, and coalescence, $A+A\to A$, may both be exactly analyzed in one dimension. While the concentrations of $A$ particles in the two processes bear a simple relation, the inter-particle distribution functions (IPDF) exhibit remarkable differences. However, the IPDF is known exactly only for the coalescence process. We obtain the IPDF for the annihilation process, based on the Glauber spin approach and assuming that the IPDF's of nearest-particle pairs are statistically independent. This assumption is supported by computer simulations. Our analysis sheds further light on the relationship between the annihilation and the coalescence models.

15 pages, plain TeX, 3 figures - available upon request (snail mail)

References in corpus (2)

• Model of Cluster Growth and Phase Separation: Exact Results in One Dimension
• Discrete to Continuous-Time Crossover due to Anisotropy in Diffusion-Limited Two-Particle Annihilation Reactions

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