# Memory-Controlled Annihilation Reactions

Source: [Memory-Controlled Annihilation Reactions](<https://www.sota2.com/research/paper/68fa1e427a2b558e29321384>)

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

Data updated: 2025-10-23T14:34:19.135Z

Authors: Steffen Trimper, Knud Zabrocki, Michael Schulz

Published: 2003-03-18T10:31:13.000Z

## Abstract

We consider a diffusion-limited reaction in case the reacting entities are not available simultaneously. Due to the fact that the reaction takes place after a spatiotemporal accumulation of reactants, the underlying rate equation has to be modified by additional non-local terms. Owing to the delay effects a finite amount of reactants remains localized, preventing a further reaction and the asymptotic decay is terminated at a finite density. The resulting inhomogeneous non-zero stationary concentration is stable against long wave length fluctuations. Below a critical wave vector $k\_c$ the system becomes inert, whereas a complete decay is realized above $k\_c$. The phase diagram for the one species-annihilation process $A + A \\to 0$ exhibits a behavior comparable to a second order phase transition. Obviously the memory effects are equivalent to long range interaction and the non-local kinetics is basically independent on space dimensions.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0303336>)

[PDF](<https://arxiv.org/pdf/cond-mat/0303336.pdf>)