Remarks on the multi-species exclusion process with reflective boundaries

Abstract

We investigate one of the simplest multi-species generalizations of the one dimensional exclusion process with reflective boundaries. The Markov matrix governing the dynamics of the system splits into blocks (sectors) specified by the number of particles of each kind. We find matrices connecting the blocks in a matrix product form. The procedure (generalized matrix ansatz) to verify that a matrix intertwines blocks of the Markov matrix was introduced in the periodic boundary condition, which starts with a local relation [Arita et al, J. Phys. A 44, 335004 (2011)]. The solution to this relation for the reflective boundary condition is much simpler than that for the periodic boundary condition.

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Cited by in corpus (4)

• Open two-species exclusion processes with integrable boundaries
• Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory
• Matrix product solution to a 2-species TASEP with open integrable boundaries
• Probability distributions of multi-species q-TAZRP and ASEP as double cosets of parabolic subgroups