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.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- April 2018
- DOI:
- 10.1088/1751-8121/aab0f4
- arXiv:
- arXiv:1711.01248
- Bibcode:
- 2018JPhA...51n5001T
- Keywords:
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- Condensed Matter - Statistical Mechanics
- E-Print:
- 24 pages, 9 figures