Integrable boundary conditions for multi-species ASEP

Abstract

The first result of the present paper is to provide classes of explicit solutions for integrable boundary matrices for the multi-species ASEP with an arbitrary number of species. All the solutions we have obtained can be seen as representations of a new algebra that contains the boundary Hecke algebra. The boundary Hecke algebra is not sufficient to build these solutions. This is the second result of our paper.

arXiv comment20 pages

References in corpus (19)

• Statistical Physics of Vehicular Traffic and Some Related Systems
• Phase transitions in an exactly soluble one-dimensional exclusion process
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models
• The Blob Algebra and the Periodic Temperley-Lieb Algebra
• Asymmetric Simple Exclusion Process with Open Boundaries and Askey-Wilson Polynomials
• Exact Current Statistics of the ASEP with Open Boundaries
• On an algebraic approach to higher dimensional statistical mechanics
• Matrix Product Eigenstates for One-Dimensional Stochastic Models and Quantum Spin Chains
• Integrable approach to simple exclusion processes with boundaries. Review and progress
• Solutions of the reflection equation for face and vertex models associated with $A_n^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ and $A_n^{(2)}$
• Two-Species Asymmetric Simple Exclusion Process with Open Boundaries
• Non-diagonal solutions to reflection equations in $su(n)$ spin chains
• Classification of reflection matrices related to (super) Yangians and application to open spin chain models
• Multispecies TASEP and the tetrahedron equation
• Let's Baxterise
• Boundary non-local charges from the open spin chain
• Baxterization of solutions to reflection equation with Hecke R-matrix
• Spectral Decomposition and Baxterisation of Exotic Bialgebras and Associated Noncommutative Geometries

Cited by in corpus (13)

• Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states
• An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
• Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries
• Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory
• The exact phase diagram for a class of multispecies asymmetric exclusion processes
• Two-species TASEP model: from a simple description to intermittency and travelling traffic jams
• Matrix product solution of a left-permeable two-species asymmetric exclusion process
• KPZ fluctuations in finite volume
• Dependence of the transportation time on the sequence in which particles with different hopping probabilities enter a lattice
• The phase diagram for a multispecies left-permeable asymmetric exclusion process
• Multi species asymmetric simple exclusion process with impurity activated flips
• The phase diagram for a class of multispecies permissive asymmetric exclusion processes
• Triangular solutions to the reflection equation for $U_q(\widehat{s{l}_n})$