# Kinetics of Heterogeneous Single-Species Annihilation

Source: [Kinetics of Heterogeneous Single-Species Annihilation](<https://www.sota2.com/research/paper/68fa24172c2a37601939f5a4>)

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

Data updated: 2025-10-24T07:57:45.414Z

Authors: P. L. Krapivsky, E. Ben-Naim, S. Redner

Published: 1994-06-27T21:59:43.000Z

## Abstract

We investigate the kinetics of diffusion-controlled heterogeneous single-species annihilation, where the diffusivity of each particle may be different. The concentration of the species with the smallest diffusion coefficient has the same time dependence as in homogeneous single-species annihilation, A+A--\>0. However, the concentrations of more mobile species decay as power laws in time, but with non-universal exponents that depend on the ratios of the corresponding diffusivities to that of the least mobile species. We determine these exponents both in a mean-field approximation, which should be valid for spatial dimension d\>2, and in a phenomenological Smoluchowski theory which is applicable in d\<2. Our theoretical predictions compare well with both Monte Carlo simulations and with time series expansions.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9406109>)

[PDF](<https://arxiv.org/pdf/cond-mat/9406109.pdf>)