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We explore the reflection-transmission quantum Yang-Baxter equations, arising in factorized scattering theory of integrable models with impurities. The physical origin of these equations is clarified and three general families of solutions…

High Energy Physics - Theory · Physics 2009-11-10 V. Caudrelier , M. Mintchev , E. Ragoucy , P. Sorba

A connection between integrability properties and general statistical properties of the spectra of symmetric transfer matrices of the asymmetric eight-vertex model is studied using random matrix theory (eigenvalue spacing distribution and…

Condensed Matter · Physics 2009-10-28 H. Meyer , J. -C. Anglès d'Auriac , J. -M. Maillard

The formal derivatives of the Yang-Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differential equations. The derivatives of the $R$ matrix…

Exactly Solvable and Integrable Systems · Physics 2021-07-07 R. S. Vieira , A. Lima-Santos

We show that the one dimensional, critical transverse field Ising model is Yang-Baxter integrable. This is done by constructing commuting transfer matrices built out of a $R$-matrix satisfying the Yang-Baxter equation with additive spectral…

High Energy Physics - Theory · Physics 2025-10-13 Akash Sinha , Tinu Justin , Pramod Padmanabhan , Vladimir Korepin

We present a solution method for the integrable system (derivative nonlinear Schr\"odinger II system) or the Chen--Lee--Liu system. This is done by presenting a solution technique for the inverse scattering problem for the corresponding…

Exactly Solvable and Integrable Systems · Physics 2025-07-30 Mehmet Unlu

We show the relationship between the strongly non-linear limit (also termed the dispersionless or the Whitham limit) of the macroscopic fluctuation theory of certain statistical models and the inverse scattering method. We show that in the…

Statistical Mechanics · Physics 2023-08-08 Eldad Bettelheim

The Quantum Inverse Scattering Method is a scheme for solving integrable models in $1+1$ dimensions, building on an $R$-matrix that satisfies the Yang--Baxter equation and in terms of which one constructs a commuting family of transfer…

Mathematical Physics · Physics 2023-07-13 Xavier Poncini , Jorgen Rasmussen

We show that an inverse scattering problem for a semilinear wave equation can be solved on a manifold having an asymptotically Minkowskian infinity, that is, scattering functionals determine the topology, differentiable structure, and the…

Analysis of PDEs · Mathematics 2025-01-17 Spyros Alexakis , Hiroshi Isozaki , Matti Lassas , Teemu Tyni

A generalised inverse scattering method has been developed for arbitrary n dimensional Lax equations. Subsequently, the method has been used to obtain N soliton solutions of a vector higher order nonlinear Schrodinger equation, proposed by…

solv-int · Physics 2009-10-31 Sasanka Ghosh , Sudipta Nandy

The paper derived differential equations which solve the problem of restoration the motion parameters for a rigid reference frame from the known proper acceleration and angular velocity of its origin as functions of proper time. These…

General Relativity and Quantum Cosmology · Physics 2023-04-18 Vitaliy Voytik

We pursue our study of the antiperiodic dynamical 6-vertex model using Sklyanin's separation of variables approach, allowing in the model new possible global shifts of the dynamical parameter. We show in particular that the spectrum and…

Mathematical Physics · Physics 2016-04-20 D. Levy-Bencheton , G. Niccoli , V. Terras

Using the Quantum Inverse Scattering Method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six vertex model with reflecting end.

solv-int · Physics 2009-10-31 O. Tsuchiya

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

Computational Engineering, Finance, and Science · Computer Science 2018-12-04 Ivan Dokmanić , Joan Bruna , Stéphane Mallat , Maarten de Hoop

A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an…

High Energy Physics - Theory · Physics 2009-10-31 J. M. Maillet , V. Terras

Correlation functions of the six and nineteen vertex models on an N \times N lattice with domain wall boundary conditions are studied. The general expression of the boundary correlation functions is obtained for the six vertex model by use…

Mathematical Physics · Physics 2011-08-02 Kohei Motegi

We derive an analog of the master equation obtained recently for correlation functions of the XXZ chain for a wide class of quantum integrable systems described by the R-matrix of the six-vertex model, including in particular continuum…

High Energy Physics - Theory · Physics 2011-02-16 N. Kitanine , K. Kozlowski , J. M. Maillet , N. A. Slavnov , V. Terras

We define an integrable lattice model which, in the notation of Yang, in addition to the conventional 2-particle $R$-matrices also contains non-reducible 3-particle $R$-matrices. The corresponding modified Yang-Baxter equations are solved…

Statistical Mechanics · Physics 2007-05-23 J. Ambjorn , Sh. Khachatryan , A. Sedrakyan

We consider a rational six vertex model on a rectangular lattice with boundary conditions that generalize the usual domain wall type. We find that the partition function of the inhomogeneous version of this model is given by a modified…

Mathematical Physics · Physics 2024-01-10 S. Belliard , R. A. Pimenta , N. A. Slavnov

In this paper the inverse scattering problem for the nonstationary Dirac-type system on the whole plane was considered. A nonlinear evolution sytem of equation related to nonstationary Dirac-type system is introduced and the solviblity of…

Mathematical Physics · Physics 2009-08-20 Mansur I Ismailov

In this paper we derive from arguments of string scattering a set of eight tetrahedron equations, with different index orderings. It is argued that this system of equations is the proper system that represents integrable structures in three…

q-alg · Mathematics 2009-10-30 Jarmo Hietarinta , Frank Nijhoff