# Disorder-Induced Anomalous Kinetics in the $A+A \\to \\emptyset$ Reaction

Source: [Disorder-Induced Anomalous Kinetics in the $A+A \\to \\emptyset$ Reaction](<https://www.sota2.com/research/paper/68fa246c2c2a3760193a3e4e>)

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

Data updated: 2025-10-24T09:10:57.035Z

Authors: Jeong-Man Park, Michael W. Deem

Published: 1997-07-11T04:31:39.000Z

## Abstract

We address the two-dimensional bimolecular annihilation reaction $A + A \\to \\emptyset$ in the presence of random impurities. Impurities with sufficiently long-ranged interaction energies are known to lead to anomalous diffusion, $\<r^2(t)\> \\sim t^{1-\\delta}$, in the absence of reaction. Applying renormalization group theory to a field theoretic description of this reaction, we find that this disorder also leads to anomalous kinetics in the long time limit: $c(t) \\sim t^{\\delta -1}$. This kinetics results because the disorder forces the system into the (sub)diffusion controlled regime, in which the kinetics must become anomalous.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9707116>)

[PDF](<https://arxiv.org/pdf/cond-mat/9707116.pdf>)