Stochastic Ballistic Annihilation and Coalescence
Abstract
We study a class of stochastic ballistic annihilation and coalescence models with a binary velocity distribution in one dimension. We obtain an exact solution for the density which reveals a universal phase diagram for the asymptotic density decay. By universal we mean that all models in the class are described by a single phase diagram spanned by two reduced parameters. The phase diagram reveals four regimes, two of which contain the previously studied cases of ballistic annihilation. The two new phases are a direct consequence of the stochasticity. The solution is obtained through a matrix product approach and builds on properties of a q-deformed harmonic oscillator algebra.
Keywords
Cite
@article{arxiv.cond-mat/0005072,
title = {Stochastic Ballistic Annihilation and Coalescence},
author = {R. A. Blythe and M. R. Evans and Y. Kafri},
journal= {arXiv preprint arXiv:cond-mat/0005072},
year = {2009}
}
Comments
4 pages RevTeX, 3 figures; revised version with some corrections, additional discussion and in RevTeX format