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.

19 pages; typos corrected, more details on the Matrix Ansatz algebra

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Cited by in corpus (22)

• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Matrix product formula for Macdonald polynomials
• Open two-species exclusion processes with integrable boundaries
• Integrable dissipative exclusion process: Correlation functions and physical properties
• Switching interacting particle systems: scaling limits, uphill diffusion and boundary layer
• Matrix product solution to a 2-species TASEP with open integrable boundaries
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• The exact phase diagram for a class of multispecies asymmetric exclusion processes
• Combinatorial mappings of exclusion processes
• Matrix product solution of a left-permeable two-species asymmetric exclusion process
• Integrability of two-species partially asymmetric exclusion processes
• $T$-$Q$ relations for the integrable two-species asymmetric simple exclusion process with open boundaries
• Dependence of the transportation time on the sequence in which particles with different hopping probabilities enter a lattice
• Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP
• Self-duality and shock dynamics in the $n$-component priority ASEP
• Matrix Product representation of the stationary state of the open Zero Range Process
• The phase diagram for a multispecies left-permeable asymmetric exclusion process
• The phase diagram for a class of multispecies permissive asymmetric exclusion processes
• Inhomogeneous discrete-time exclusion processes
• Integrability in out-of-equilibrium systems
• Matrix product solution of the stationary states of two-species open zero range processes
• Triangular solutions to the reflection equation for $U_q(\widehat{s{l}_n})$