Diffusion-Limited One-Species Reactions in the Bethe Lattice
Daniel ben-Avraham, M. Lawrence Glasser
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 ρ2 (ρis the particle density), initially, when the particles are uncorrelated, to [(z-2)/z]ρ2, 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.
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