Integrable approach to simple exclusion processes with boundaries. Review and progress (Q3301819)

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

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scholarly article

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

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Nicolas Crampé

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Matthieu Vanicat

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Journal of Statistical Mechanics: Theory and Experiment

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publication date

11 August 2020

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full work available at URL

https://arxiv.org/abs/1408.5357

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MaRDI profile type

MaRDI publication profile

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Exact solution of a 1D asymmetric exclusion model using a matrix formulation

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Nonequilibrium steady states of matrix-product form: a solver's guide

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Boundary conditions for integrable quantum systems

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Stationary State of Integrable Systems in Matrix Product Form

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BOUNDARY S MATRIX AND BOUNDARY STATE IN TWO-DIMENSIONAL INTEGRABLE QUANTUM FIELD THEORY

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Exact solution of XXZ spin chain with unparallel boundary fields

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The complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms

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Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables

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Matrix product eigenstates for one-dimensional stochastic models and quantum spin chains

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Diffusion algebras

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On matrix product ground states for reaction - diffusion models

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The matrix product solution of the multispecies partially asymmetric exclusion process

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Matrix representation of the stationary measure for the Multispecies TASEP

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Recursive structures in the multispecies TASEP

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Generalized matrix Ansatz in the multispecies exclusion process—the partially asymmetric case

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Construction of a matrix product stationary state from solutions of a finite-size system

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Quantum inverse problem method. I

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Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction

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Partition function of the eight-vertex lattice model

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Solutions of the Yang-Baxter equation

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Integrable three-state vertex models with weights lying on genus five curves

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On the solutions to the multi-parametric Yang-Baxter equations

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Quantum R matrix for the generalized Toda system

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Factorizing particles on a half-line and root systems

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Boundary K-matrices for the six vertex and the n(2n-1)A<sub>n-1</sub>vertex models

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Boundary K-matrices for the XYZ, XXZ and XXX spin chains

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Reflection \(K\)-matrices for \(19\)-vertex models.

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Classification of reflection matrices related to (super-)Yangians and application to open spin chain models

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General boundary conditions for the and open spin chains

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Twisted yangians and infinite-dimensional classical Lie algebras

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Yangians and classical Lie algebras

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COIDEAL SUBALGEBRAS IN QUANTUM AFFINE ALGEBRAS

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REPRESENTATIONS OF REFLECTION ALGEBRAS

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Reflection equation and twisted Yangians

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Quantum group symmetry in sine-Gordon and affine Toda field theories on the half-line

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Boundary remnant of Yangian symmetry and the structure of rational reflection matrices

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Coideal algebras from twisted Manin triples

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Integrable boundary conditions for a non-Abelian anyon chain with \(D(D_{3})\) symmetry

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Integrable open boundary conditions for \(XXC\) models

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Algebraic Bethe ansatz for open XXX model with triangular boundary matrices

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Algebraic Bethe ansatz for the six vertex model with upper triangular<i>K</i>-matrices

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Heisenberg XXX model with general boundaries: eigenvectors from algebraic Bethe ansatz

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Representation of the Zamolodchikov-Faddeev algebra

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Creation/annihilation operators and form factors of the \(XXZ\) model

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Vertex operators for boundary algebras

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Vertex operators for quantum groups and application to integrable systems

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\(T\)-\(Q\) relation and exact solution for the \(XYZ\) chain with general non-diagonal boundary terms

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Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy.

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Connected operators for the totally asymmetric exclusion process

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Solution of the \(\text{SU}(N)\) vertex model with non-diagonal open boundaries

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Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries

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Bethe ansatz for the \(XXX\)-\(S\) chain with non-diagonal open boundaries

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Functional relations and Bethe Ansatz for the \(XXZ\) chain

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Bethe ansatz solution of the open XXZ chain with nondiagonal boundary terms

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Bethe ansatz derived from the functional relations of the open<i>XXZ</i>chain for new special cases

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Solving the open \(XXZ\) spin chain with nondiagonal boundary terms at roots of unity

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Construction of a coordinate Bethe ansatz for the asymmetric simple exclusion process with open boundaries

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Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms

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\(Q\)-operator and \(T\)-\(Q\) relation from the fusion hierarchy

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Matrix coordinate Bethe Ansatz: applications to XXZ and ASEP models

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Matrix ansatz for the fluctuations of the current in the ASEP with open boundaries

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Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions

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An inhomogeneous<i>T</i>-<i>Q</i>equation for the open XXX chain with general boundary terms: completeness and arbitrary spin

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Exact spectrum of the XXZ open spin chain from the<i>q</i>-Onsager algebra representation theory

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Functional relations from the Yang-Baxter algebra: Eigenvalues of the \(XXZ\) model with non-diagonal twisted and open boundary conditions

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Separation of variables in the open \(XXX\) chain

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Non-diagonal open spin-1/2<i>X</i><i>X</i><i>Z</i>quantum chains by separation of variables: complete spectrum and matrix elements of some quasi-local operators

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Bethe Ansatz and<i>Q</i>-operator for the open ASEP

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Off-diagonal Bethe ansatz solutions of the anisotropic spin-\(\frac{1}{2}\) chains with arbitrary boundary fields

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Identifiers

zbMATH Open document ID

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10.1088/1742-5468/2014/11/P11032

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:3301819

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