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

Source: [Diffusion-Limited One-Species Reactions in the Bethe Lattice](<https://www.sota2.com/research/paper/68fa20d57a2b558e29333941>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T23:10:32.577Z

Authors: Daniel ben-Avraham, M. Lawrence Glasser

Published: 2006-12-04T15:32:57.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0612089>)

[PDF](<https://arxiv.org/pdf/cond-mat/0612089.pdf>)