Journal Articles Journal of Physics A: Mathematical and Theoretical Year : 2015

Open two-species exclusion processes with integrable boundaries

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.

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hal-01157694 , version 1 (07-02-2019)

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Nicolas Crampé, Kirone Mallick, Eric Ragoucy, Matthieu Vanicat. Open two-species exclusion processes with integrable boundaries. Journal of Physics A: Mathematical and Theoretical, 2015, 48 (17), pp.175002. ⟨10.1088/1751-8113/48/17/175002⟩. ⟨hal-01157694⟩
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