Integrable approach to simple exclusion processes with boundaries. Review and progress

Abstract

We study the matrix ansatz in the quantum group framework, applying integrable systems techniques to statistical physics models. We start by reviewing the two approaches, and then show how one can use the former to get new insight on the latter. We illustrate our method by solving a model of reaction-diffusion. An eigenvector for the transfer matrix for the XXZ spin chain with non-diagonal boundary is also obtained using a matrix ansatz.

44 pages

References in corpus (16)

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• Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
• Separation of Variables in the open XXX chain
• Matrix representation of the stationary measure for the multispecies TASEP
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
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• On the solutions to the multi-parametric Yang-Baxter equations
• R-matrices of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
• The Yang-Baxter equation for PT invariant nineteen vertex models
• Construction of a matrix product stationary state from solutions of finite size system
• Connected Operators for the Totally Asymmetric Exclusion Process
• Reflection equation and twisted Yangians
• Retrieve the Bethe states of quantum integrable models solved via off-diagonal Bethe Ansatz

Cited by in corpus (42)

• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Stochastic $R$ matrix for $U_q(A_n^{(1)})$
• Matrix product formula for Macdonald polynomials
• Open two-species exclusion processes with integrable boundaries
• Multispecies TASEP and the tetrahedron equation
• Correlators of double scaled SYK at one-loop
• Duality and hidden equilibrium in transport models
• Non-compact quantum spin chains as integrable stochastic particle processes
• 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
• Integrable dissipative exclusion process: Correlation functions and physical properties
• Integrable boundary conditions for multi-species ASEP
• Integrable Floquet dynamics, generalized exclusion processes and "fused" matrix ansatz
• Exact solution of an integrable non-equilibrium particle system
• Algebraic Bethe ansatz for the totally asymmetric simple exclusion process with boundaries
• Matrix product solution to a 2-species TASEP with open integrable boundaries
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Combinatorial mappings of exclusion processes
• Eigenstates of triangularisable open XXX spin chains and closed-form solutions for the steady state of the open SSEP
• Equivalent T-Q relations and exact results for the open TASEP
• Matrix product solution to multi-species ASEP with open boundaries
• Boundary matrices for the higher spin six vertex model
• Matrix product solution of a left-permeable two-species asymmetric exclusion process
• A new braid-like algebra for Baxterisation
• Matrix product solution for a partially asymmetric 1D lattice gas with a free defect
• Stochastic strong zero modes and their dynamical manifestations
• Matrix product formula for $U_q(A_2^{(1)})$-zero range process
• Integrability of two-species partially asymmetric exclusion processes
• 3-state Hamiltonians associated to solvable 33-vertex models
• A $q$-boson representation of Zamolodchikov-Faddeev algebra for stochastic $R$ matrix of $U_q(A_n^{(1)})$
• Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP
• Integrable Structure of Multispecies Zero Range Process
• Inhomogeneous discrete-time exclusion processes
• Integrability in out-of-equilibrium systems
• The steady state of the boundary-driven multiparticle asymmetric diffusion model
• Holographic tensor network for double-scaled SYK
• A stochastic model solvable without integrability
• Triangular solutions to the reflection equation for $U_q(\widehat{s{l}_n})$
• Steady state representations for the harmonic process
• Bi-orthogonal Polynomials and the Five parameter Asymmetric Simple Exclusion Process
• Invariant measures of discrete interacting particle systems: Algebraic aspects
• Bi-orthogonal Polynomial Sequences and the Asymmetric Simple Exclusion Process