---
title: Fast-diffusion mean-field theory for k-body reactions in one dimension
description:   We derive an improved mean-field approximation for k-body annihilation
reactions kA --> inert, for hard-core diffusing particles on a line,
annihilating in groups of k neighbors with probability 0 < q <= 1. The hopping
and annihilation processes are correlated to mimic chemical reactions. Our new
mean-field theory accounts for hard-core particle properties and has a larger
region of applicability than the standard chemical rate equation especially for
large k values. Criteria for validity of the mean-field theory and its use in
phenomenological data fits are derived. Numerical tests are reported for
k=3,4,5,6.

url: https://modelslab.com/ai-news/fast-diffusion-mean-field-theory-for-k-body-reactions-in-one-dimension
canonical: https://modelslab.com/ai-news/fast-diffusion-mean-field-theory-for-k-body-reactions-in-one-dimension
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generated_at: 2026-01-20T14:32:30.528636Z
---

# Fast-diffusion mean-field theory for k-body reactions in one dimension

>   We derive an improved mean-field approximation for k-body annihilation
reactions kA --> inert, for hard-core diffusing particles on a line,
annihilating in groups of k neighbors with probability 0 < q <= 1. The hopping
and annihilation processes are correlated to mimic chemical reactions. Our new
mean-field theory accounts for hard-core particle properties and has a larger
region of applicability than the standard chemical rate equation especially for
large k values. Criteria for validity of the mean-field theory and its use in
phenomenological data fits are derived. Numerical tests are reported for
k=3,4,5,6.



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