Diffusion-Limited One-Species Reactions in the Bethe Lattice
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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.
To be published in JPCM, special issue on Kinetics of Chemical Reactions
To be published in JPCM, special issue on Kinetics of Chemical Reactions