Related papers: A Factorization of the S-Matrix into Jost Matrices
The scattering matrix for the full-line matrix Schr\"odinger equation is analyzed when the corresponding matrix-valued potential is selfadjoint, integrable, and has a finite first moment. The matrix-valued potential is decomposed into a…
The restriction imposed on the J-matrix method of using specific L2 bases is lifted without compromising any of the advantages that it offers. This opens the door to a wider range of application of the method to physical problems beyond the…
The multichannel scattering problem for the stationary Schr\"{o}dinger equation on a line with different thresholds at both infinities is investigated. The analytical structure of the Jost solutions and of the transition matrix relating the…
We show that the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe…
The relativistic version of the J-matrix method for a scattering problem on the potential vanishing faster than the Coulomb one is formulated. As in the non-relativistic case it leads to a finite algebraic eigenvalue problem. The derived…
Let $R$ be a commutative unital ring. A well-known factorization problem is whether any matrix in $\mathrm{SL}_n(R)$ is a product of elementary matrices with entries in $R$. To solve the problem, we use two approaches based on the notion of…
We study systematically a matrix Riemann-Hilbert problem for the modified Landau-Lifshitz (mLL) equation with nonzero boundary conditions at infinity. Unlike the zero boundary conditions case, there occur double-valued functions during the…
The asymptotic behaviour of the superpotential of general SUSY transformations for a coupled-channel Hamiltonian with different thresholds is analyzed. It is shown that asymptotically the superpotential can tend to a diagonal matrix with an…
A new concept of meromorphic $\Sigma$-factorization, for H\"{o}lder continuous functions defined on a contour $\Gamma$ that is the pullback of $\dot{\mathbb{R}}$ (or the unit circle) in a Riemann surface $\Sigma$ of genus 1, is introduced…
Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We…
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…
It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the…
Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…
Supersymmetric (SUSY) transformations of the multi-channel Schr\"odinger equation with equal thresholds and arbitrary partial waves in all channels are studied. The structures of the transformation function and the superpotential are…
We obtain a tight, up to a logarithmic factor, upper bound on the number of solutions to the equation $$ \sum_{j=1}^n a_j \frac{s_j}{r_j} =a_0, \qquad $$ with variables $r_1,...,r_n$ in an arbitrary box at the origin and variables $s_1,...,…
The inverse scattering method within the $J$-matrix approach to the two coupled-channel problem is discussed. We propose a generalization of the procedure to the case with different thresholds.
This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
The inverse scattering transform for a special case of the 3-wave resonant interaction equations with non-vanishing boundary conditions is studied. The Jost solutions and the fundamental analytic solutions (FAS) for the associated spectral…
Supervised classification and representation learning are two widely used classes of methods to analyze multivariate images. Although complementary, these methods have been scarcely considered jointly in a hierarchical modeling. In this…