Diffusion-Limited One-Species Reactions in the Bethe Lattice

Details Diffusion-Limited One-Species Reactions in the Bethe Lattice Diffusion-Limited One-Species Reactions in the Bethe Lattice

2006-12-04

arxiv.org/abs/cond-mat/0612089v1

J. Phys.: Condens. Matter 19, 065107 (2007)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/0953-8984/19/6/065107

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.

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