Reaction-diffusion on the fully-connected lattice: $A+A\rightarrow A$
| Autor: | Turban, L., Fortin, J. -Y. |
|---|---|
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | J. Phys. A 51 (2018) 145001 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8121/aab0f4 |
| Popis: | 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. Comment: 24 pages, 9 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|