Diffusion algebras
Statistical Mechanics
2009-11-07 v2 Quantum Algebra
Abstract
We define the notion of "diffusion algebras". They are quadratic Poincare-Birkhoff-Witt (PBW) algebras which are useful in order to find exact expressions for the probability distributions of stationary states appearing in one-dimensional stochastic processes with exclusion. One considers processes in which one has N species, the number of particles of each species being conserved. All diffusion algebras are obtained. The known examples already used in applications are special cases in our classification. To help the reader interested in physical problems, the cases N=3 and 4 are listed separately.
Cite
@article{arxiv.cond-mat/0103603,
title = {Diffusion algebras},
author = {A. P. Isaev and P. N. Pyatov and V. Rittenberg},
journal= {arXiv preprint arXiv:cond-mat/0103603},
year = {2009}
}
Comments
29 pages; minor misprints corrected, few references added