Open two-species exclusion processes with integrable boundaries

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...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2015-05, Vol.48 (17), p.175002-18
Main Authors: Crampe, N, Mallick, K, Ragoucy, E, Vanicat, M
Format: Article
Language:English
Subjects:
Asymmetry
Boundaries
Boundary conditions
Classification
Condensed Matter
Construction specifications
Density
Exactly Solvable and Integrable Systems
exclusion process
integrabilty
Mathematical models
Mathematical Physics
Mathematics
matrix ansatz
Nonlinear Sciences
Particles (of physics)
Physics
Statistical Mechanics
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Summary: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 nine generators) is explicitly constructed and physical observables (such as currents, densities) calculated.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/48/17/175002