Finitedimensional representations of the quadratic algebra: Applications to the exclusion process
Abstract
We study the onedimensional partially asymmetric simple exclusion process (ASEP) with open boundaries, that describes a system of hardcore particles hopping stochastically on a chain coupled to reservoirs at both ends. Derrida and coworkers showed in 1993 that the stationary probability distribution of this model can be represented as a trace on a quadratic algebra, closely related to the deformed oscillatoralgebra. We construct all finitedimensional irreducible representations of this algebra. This enables us to compute the stationary bulk density as well as all correlation lengths for the ASEP on a set of special curves of the phase diagram.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 July 1997
 DOI:
 10.1088/03054470/30/13/008
 arXiv:
 arXiv:condmat/9705152
 Bibcode:
 1997JPhA...30.4513M
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 18 pages, Latex, 1 EPS figure