Diffusion-Limited One-Species Reactions in the Bethe Lattice
Statistical Mechanics
2007-05-23 v1
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 \rho^2 (\rho is the particle density), initially, when the particles are uncorrelated, to [(z-2)/z]\rho^2, in the long-time asymptotic limit. As a result, the particle density decays inversely proportional to time, \rho ~ 1/kt, but at a rate k that slowly decreases to an asymptotic constant value.
Cite
@article{arxiv.cond-mat/0612089,
title = {Diffusion-Limited One-Species Reactions in the Bethe Lattice},
author = {Daniel ben-Avraham and M. Lawrence Glasser},
journal= {arXiv preprint arXiv:cond-mat/0612089},
year = {2007}
}
Comments
To be published in JPCM, special issue on Kinetics of Chemical Reactions