Open two-species exclusion processes with integrable boundaries
Statistical Mechanics
2015-08-03 v2 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We give a complete classification of integrable Markovian boundary conditions for the asymmetric simple exclusion process with two species (or classes) of particles. Some of these boundary conditions lead to non-vanishing particle currents for each species. We explain how the stationary state of all these models can be expressed in a matrix product form, starting from two key components, the Zamolodchikov-Faddeev and Ghoshal-Zamolodchikov relations. This statement is illustrated by studying in detail a specific example, for which the matrix Ansatz (involving 9 generators) is explicitly constructed and physical observables (such as currents, densities) calculated.
Cite
@article{arxiv.1412.5939,
title = {Open two-species exclusion processes with integrable boundaries},
author = {N. Crampe and K. Mallick and E. Ragoucy and M. Vanicat},
journal= {arXiv preprint arXiv:1412.5939},
year = {2015}
}
Comments
19 pages; typos corrected, more details on the Matrix Ansatz algebra