2014/12/31 by N. Crampe, K. Mallick, E. Ragoucy +1 · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1088/1751-8113/48/17/175002
published as J. Phys. A: Math. Theor. 48 (2015) 175002 · 19 pages; typos corrected, more details on the Matrix Ansatz algebra
arxiv created 2015/03/17 · arxiv updated 2015/08/03
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.