Reaction-diffusion on the fully-connected lattice: $A+A\rightarrow A$
Abstract
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.
Cite
@article{arxiv.1711.01248,
title = {Reaction-diffusion on the fully-connected lattice: $A+A\rightarrow A$},
author = {L. Turban and J. -Y. Fortin},
journal= {arXiv preprint arXiv:1711.01248},
year = {2018}
}
Comments
24 pages, 9 figures