Inhomogeneous discrete-time exclusion processes
Statistical Mechanics
2015-10-30 v2 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We study discrete time Markov processes with periodic or open boundary conditions and with inhomogeneous rates in the bulk. The Markov matrices are given by the inhomogeneous transfer matrices introduced previously to prove the integrability of quantum spin chains. We show that these processes have a simple graphical interpretation and correspond to a sequential update. We compute their stationary state using a matrix ansatz and express their normalization factors as Schur polynomials. A connection between Bethe roots and Lee-Yang zeros is also pointed out.
Cite
@article{arxiv.1506.04874,
title = {Inhomogeneous discrete-time exclusion processes},
author = {N. Crampe and K. Mallick and E. Ragoucy and M. Vanicat},
journal= {arXiv preprint arXiv:1506.04874},
year = {2015}
}
Comments
30 pages, 10 figures; a short paragraph at the end to justify the form of the sequential update has been added; the justification of the transfer matrix degree is detailed