Diffusion-Limited One-Species Reactions in the Bethe Lattice

Abstract

We study the kinetics of diffusion-limited coalescence, A+A-->A, and annihilation, A+A-->0, in the Bethe lattice of coordination number z. Correlations build up over time so that the probability to find a particle next to another varies from ρ^2 (ρis the particle density), initially, when the particles are uncorrelated, to [(z-2)/z]ρ^2, in the long-time asymptotic limit. As a result, the particle density decays inversely proportional to time, ρ~ 1/kt, but at a rate k that slowly decreases to an asymptotic constant value.

arXiv commentTo be published in JPCM, special issue on Kinetics of Chemical Reactions

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• Exact correlation functions in particle-reaction models with immobile particles
• Reaction-diffusion on the fully-connected lattice: $A+A\to A$