Continued Fractions and the Partially Asymmetric Exclusion Process
Statistical Mechanics
2009-07-27 v1 Mathematical Physics
Combinatorics
math.MP
Abstract
We note that a tridiagonal matrix representation of the algebra of the partially asymmetric exclusion process (PASEP) lends itself to interpretation as the transfer matrix for weighted Motzkin lattice paths. A continued fraction ("J-Fraction") representation of the lattice path generating function is particularly well suited to discussing the PASEP, for which the paths have height dependent weights. We show that this not only allows a succinct derivation of the normalisation and correlation lengths of the PASEP, but also reveals how finite-dimensional representations of the PASEP algebra, valid only along special lines in the phase diagram, relate to the general solution that requires an infinite-dimensional representation.
Keywords
Cite
@article{arxiv.0904.3947,
title = {Continued Fractions and the Partially Asymmetric Exclusion Process},
author = {R. A. Blythe and W. Janke and D. A. Johnston and R. Kenna},
journal= {arXiv preprint arXiv:0904.3947},
year = {2009}
}