Diffusion algebras

Details Diffusion algebras Diffusion algebras

2001-03-29

arxiv.org/abs/cond-mat/0103603v2

Physics

Condensed Matter

Statistical Mechanics

29 pages; minor misprints corrected, few references added

Scientific paper

10.1088/0305-4470/34/29/306

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.

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