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We present a multiple-scattering model for the effective refractive index of an arbitrarily dense suspension of forward-scattering particles. The model provides a very simple formula for the effective refractive index of such a suspension…

Optics · Physics 2023-08-02 Alexander Nahmad-Rohen , Augusto García-Valenzuela

We prove a determinant formula for the standard integral form of a lattice vertex operator algebra.

Rings and Algebras · Mathematics 2019-03-21 Chongying Dong , Robert L. Griess

The six-vertex model with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is obtained. The kernel of the corrtesponding integral operator depends on Laguerre…

Condensed Matter · Physics 2007-05-23 N. A. Slavnov

We obtain the determinant representations of the scalar products for the XXZ Gaudin model with generic non-diagonal boundary terms.

Mathematical Physics · Physics 2012-05-25 Kun Hao , Wen-Li Yang , Heng Fan , Si-Yuan Liu , Ke Wu , Zhan-Ying Yang , Yao-Zhong Zhang

In this paper we consider solutions to the reflection equation related to the higher spin stochastic six vertex model. The corresponding higher spin $R$-matrix is associated with the affine quantum algebra $U_q(\widehat{sl(2)})$. The…

Mathematical Physics · Physics 2019-06-17 Vladimir V. Mangazeev , Xilin Lu

The general solutions for the factorization equations of the reflection matrices $K^{\pm}(\theta)$ for the eight vertex and six vertex models (XYZ, XXZ and XXX chains) are found. The associated integrable magnetic Hamiltonians are…

High Energy Physics - Theory · Physics 2009-10-22 H. J. de Vega , A. González--Ruiz

We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum…

Mathematical Physics · Physics 2024-06-17 Filippo Colomo , Giuseppe Di Giulio , Andrei G. Pronko

We present an inversion formula which can be used to obtain resolvent expansions near embedded thresholds. As an application, we prove for a class of quantum waveguides the absence of accumulation of eigenvalues and the continuity of the…

Mathematical Physics · Physics 2014-11-20 S. Richard , R. Tiedra de Aldecoa

Applying the inverse scattering transform to study a focusing two-component Hirota equation with nonzero boundary conditions at infinity. Through the spectral problem and the adjoint spectral problem, the analyticity properties and symmetry…

Exactly Solvable and Integrable Systems · Physics 2025-02-25 Feng Zhang , Pengfei Han , Yi Zhang

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 develop a unified method to study spectral determinants for several different manifolds, including spheres and hemispheres, and projective spaces. This is a direct consequence of an approach based on deriving recursion relations for the…

Spectral Theory · Mathematics 2025-06-30 J. Cunha , P. Freitas

In this letter, the 6-vertex model on dynamical random lattices is defined via a matrix model and rewritten (following I. Kostov) as a deformation of the O(2) model. In the large N planar limit, an exact solution is found at criticality.…

Statistical Mechanics · Physics 2010-12-17 P. Zinn-Justin

We discuss the influence of boundary conditions on the continuum limit of the six-vertex model by deriving a variational principle for the associated height function with arbitrary fixed boundary conditions. We discuss its consequences…

Statistical Mechanics · Physics 2007-05-23 P. Zinn-Justin

We consider the Quantum Inverse Scattering Method with a new R-matrix depending on two parameters $q$ and $t$. We find that the underlying algebraic structure is the two-parameter deformed algebra $SU_{q,t}(2)$ enlarged by introducing an…

High Energy Physics - Theory · Physics 2009-10-28 M. R-Monteiro , I. Roditi , L. M. C. S. Rodrigues , S. Sciuto

The main result of this paper is the construction of infinitely many conserved quantities (corresponding to commuting transfer-matrices) for the limit shape equation for the 6-vertex model on a cylinder. This suggests that the limit shape…

Mathematical Physics · Physics 2015-10-06 Nicolai Reshetikhin , Ananth Sridhar

The 2D off-critical q-state Potts model with boundaries was studied as a factorizable relativistic scattering theory. The scattering S-matrices for particles reflecting off the boundaries were obtained for the cases of ``fixed'' and…

High Energy Physics - Theory · Physics 2014-11-18 Leung Chim

We consider the massive Thirring model in the laboratory coordinates and explain how the inverse scattering transform can be developed with the Riemann-Hilbert approach. The key ingredient of our method is to transform the corresponding…

Analysis of PDEs · Mathematics 2018-10-01 Dmitry E. Pelinovsky , Aaron Saalmann

We derive and classify all solutions of the boundary Yang-Baxter equation (or the reflection equation) for the 19-vertex model associated with $U_q(\widehat{sl_2})$. Integrable $XXZ$ spin-1 chain hamiltonian with general boundary…

High Energy Physics - Theory · Physics 2009-10-30 Takeo Inami , Satoru Odake , Yao-Zhong Zhang

We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…

Optics · Physics 2012-08-23 Johannes Skaar , Magnus W. Haakestad

We derive functional equations for the eigenvalues of the XXZ model subject to anti-diagonal twisted boundary conditions by means of fusion of transfer matrices and by Sklyanin's method of separation of variables. Our findings coincide with…

High Energy Physics - Theory · Physics 2009-05-01 Sönke Niekamp , Tobias Wirth , Holger Frahm