Rethinking Private Higher Education

Cantini, Daniele

doi:10.1163/9789004291508

Cited by 17 publications

(1 citation statement)

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“…Finally, a systematic investigation of integrable boundaries for various generalizations of the exclusion processes remains an open problem. Some particularly interesting cases are the following: the 2-TASEP model with unequal hopping rates [11] (the bulk dynamics is known to be integrable [19]), the homogeneous N-species ASEP (for generic N a brute force resolution of the reflection equation seems difficult but partial results were obtained using a baxterisation of a boundary Hecke algebra [20]) and the bridge model which is variant of the 2-TASEP. The bridge model, which for some choices of boundary rates displays a fascinating spontaneous symmetry-breaking [39,47], has eluded an exact solution.…”

Section: Discussionmentioning

confidence: 99%

Open two-species exclusion processes with integrable boundaries

Crampé¹,

Mallick²,

Ragoucy³

et al. 2015

J. Phys. A: Math. Theor.

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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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