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Let $M$ be a scattering manifold, i.e., a Riemannian manifold with asymptotically conic structure, and let $H$ be a Schr\"odinger operator on $M$. We can construct a natural time-dependent scattering theory for $H$ with a suitable reference…

Analysis of PDEs · Mathematics 2012-03-28 Kenichi Ito , Shu Nakamura

The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of…

High Energy Physics - Theory · Physics 2009-10-28 G. Delfino , G. Mussardo , P. Simonetti

The problem of substructure characteristic modes is developed using a scattering matrix-based formulation, generalizing subregion characteristic mode decomposition to arbitrary computational tools. It is shown that the modes of the…

Computational Engineering, Finance, and Science · Computer Science 2025-03-13 Mats Gustafsson , Lukas Jelinek , Miloslav Capek , Johan Lundgren , Kurt Schab

We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time \pi on…

Analysis of PDEs · Mathematics 2007-05-23 T. J. Christiansen , M. S. Joshi

We investigate factorized scattering from a reflecting and transmitting impurity. Bulk scattering is non trivial, provided that the bulk scattering matrix depends separately on the spectral parameters of the colliding particles, and not…

High Energy Physics - Theory · Physics 2009-11-07 M. Mintchev , E. Ragoucy , P. Sorba

In this paper, we consider the scattering problem for a class of $N$-coupled systems of the cubic nonlinear Schr\"odinger equations in three space dimensions. We prove the scattering of solutions that have a mass-energy quantity less than…

Analysis of PDEs · Mathematics 2023-03-23 Satoshi Masaki , Ryusei Tsukuda

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 construct the classical r-matrix structure for the Lax formulation of BC_N Ruijsenaars-Schneider systems proposed in hep-th 0006004. The r-matrix structure takes a quadratic form similar to the A_N Ruijsenaars-Schneider Poisson bracket…

Exactly Solvable and Integrable Systems · Physics 2009-11-07 J. Avan , G. Rollet

We briefly review results on two-dimensional supersymmetric quantum field theories that exhibit factorizable particle scattering. Our particular focus is on a series of $N\!=\!1$ supersymmetric theories, for which exact $S$-matrices have…

High Energy Physics - Theory · Physics 2007-05-23 M. Moriconi , K. Schoutens

A deformation of the classical trigonometric BC(n) Sutherland system is derived via Hamiltonian reduction of the Heisenberg double of SU(2n). We apply a natural Poisson-Lie analogue of the Kazhdan-Kostant-Sternberg type reduction of the…

Mathematical Physics · Physics 2019-02-14 L. Feher , T. F. Gorbe

For one dimensional SU(n) Hubbard model, a pair of Lax operators are derived, which give a set of fundamental equations for the quantum inverse scattering method under both periodic and open boundary conditions. This provides another proof…

Strongly Correlated Electrons · Physics 2009-10-31 Ruihong Yue , Ryu Sasaki

We define the notion of C^{(2)}_{N+1} Ruijsenaars-Schneider models and construct their Lax formulation. They are obtained by a particular folding of the A_{2N+1} systems. Their commuting Hamiltonians are linear combinations of…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Jean Avan , Genevieve Rollet

We analyze the scattering of elliptically polarized plane waves normally incident at the planar interface between two different materials; we consider two cases: dielectric-dielectric and dielectric-conductor interfaces. The scattering…

Classical Physics · Physics 2011-04-15 M. Martínez-Mares , E. Castaño

Due to color confinement, hadrons are inseparable when studying strong interactions. The paper mainly studies the scattering in the background field, especially the scattering of quarks in the hadronic background field. We discovered that…

High Energy Physics - Theory · Physics 2024-01-17 Cong Li

We present a new case of duality between integrable many-body systems, where two systems live on the action-angle phase spaces of each other in such a way that the action variables of each system serve as the particle positions of the other…

Mathematical Physics · Physics 2014-10-28 L. Feher , T. F. Gorbe

Let $S(k)$ be the scattering matrix for a Schr\"odinger operator (Laplacian plus potential) on $\RR^n$ with compactly supported smooth potential. It is well known that $S(k)$ is unitary and that the spectrum of $S(k)$ accumulates on the…

Spectral Theory · Mathematics 2015-02-27 Jesse Gell-Redman , Andrew Hassell

Based on the Hamiltonian formalism approach, a generalized L\"uscher's formula for two particle scattering in both the elastic and coupled-channel cases in moving frames is derived from a relativistic Lippmann-Schwinger equation. Some…

High Energy Physics - Lattice · Physics 2013-08-09 Peng Guo , Jozef Dudek , Robert Edwards , Adam P. Szczepaniak

We study the coupling matrix of $\mathcal{N}=2$ $SU(N)$ gauge theories with $2N$ fundamental hypermultiplets in the special vacuum, where a residual $\mathbb{Z}_N$ symmetry restores nontrivial modular structure. Using symmetry and…

High Energy Physics - Theory · Physics 2026-05-15 Aleksei Bykov , Ekaterina Sysoeva

We consider the nonlinear Schr{\"o}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and…

Analysis of PDEs · Mathematics 2020-12-16 Rémi Carles

The unitary S-matrix for the space-time non-commutative QED is constructed using the $\star$-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, perturbation theory is formulated and Feynman…

High Energy Physics - Theory · Physics 2007-05-23 Chaiho Rim , Jae Hyung Yee