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Dynamic modulation of material properties in space and time enables powerful control over wave propagation, yet existing theories largely rely on idealized, nondispersive models. In realistic media, frequency dispersion can strongly reshape…

Optics · Physics 2026-04-02 Klaas De Kinder , Christophe Caloz

Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated…

Numerical Analysis · Mathematics 2022-07-27 Vladimir Druskin , Shari Moskow , Mikhail Zaslavsky

We introduce a perturbative formulation for a nonlinear extension of the J-matrix method of scattering in two dimensions. That is, we obtain the scattering matrix for the time-independent nonlinear Schr\"odinger equation in two dimensions…

Quantum Physics · Physics 2026-05-20 T. J. Taiwo , A. D. Alhaidari , U. Al Khawaja

We consider the scattering of time-harmonic electromagnetic waves by a penetrable thin tubular scattering object in three-dimensional free space. We establish an asymptotic representation formula for the scattered wave away from the thin…

Analysis of PDEs · Mathematics 2020-10-05 Yves Capdeboscq , Roland Griesmaier , Marvin Knöller

We investigate the inverse scattering problem for the massive Thirring model, focusing particularly on cases where the transmission coefficient exhibits $N$ pairs of higher-order poles. Our methodology involves transforming initial data…

Exactly Solvable and Integrable Systems · Physics 2024-11-28 Dongli Luan , Bo Xue , Huan Liu

We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…

Numerical Analysis · Mathematics 2020-02-03 Liliana Borcea , Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky , Jörn Zimmerling

We continue our study of scattering theory and dispersive properties for one-dimensional charge transfer models, namely linear Schr\"odinger equations with multiple moving potentials. By the discovery of a refined structure of the…

Analysis of PDEs · Mathematics 2025-10-15 Gong Chen , Abdon Moutinho

We develop a field theoretical approach based on the temporary basis description as a tool to investigate the transmission properties of a time-driven quantum device. It employs a perturbative scheme for the calculation of the transmission…

We develop a new quantum-mechanical approach to scattering a particle on a one-dimensional (1D) system of two identical rectangular potential barriers, which implies modelling the dynamics of its subprocesses -- transmission and reflection…

Quantum Physics · Physics 2015-03-17 N. L. Chuprikov

Based on our previous study [IS3] on the stationary scattering theory for the Schrodinger operator on a manifold possessing an escape function we complete our investigation by doing the time-dependent counterpart. A particular class of…

Differential Geometry · Mathematics 2019-05-09 Kenichi Ito , Erik Skibsted

These lectures treat scattering theory from a non-perturbative point of view. The course begins with a review of formal aspects in scattering theory, discussing the in/out states and the $S$ matrix that connects them. Unitarity relations,…

High Energy Physics - Phenomenology · Physics 2024-09-26 J. A. Oller

We analyse the scattering operator associated with the defocusing nonlinear Schr{\"o}dinger equation which captures the evolution of solutions over an infinite time-interval under the nonlinear flow of this equation. The asymptotic nature…

Analysis of PDEs · Mathematics 2026-04-08 Rémi Carles , Georg Maierhofer

We study the effect of discrete symmetry breaking in inhomogeneous scattering media within the framework of generic wave propagation. Our focus is on one-dimensional scattering potentials exhibiting local symmetries. We find a class of…

Quantum Physics · Physics 2015-07-22 P. A. Kalozoumis , C. Morfonios , F. K. Diakonos , P. Schmelcher

The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients…

Quantum Physics · Physics 2016-03-22 B. C. Lütfüoğlu , F. Akdeniz , O. Bayrak

We develop a definitive physical-space scattering theory for the scalar wave equation on Kerr exterior backgrounds in the general subextremal case |a|<M. In particular, we prove results corresponding to "existence and uniqueness of…

General Relativity and Quantum Cosmology · Physics 2018-06-28 Mihalis Dafermos , Igor Rodnianski , Yakov Shlapentokh-Rothman

This article is devoted to studying the inverse scattering for the fractional Schr\"{o}dinger equation, and in particular we solve the Born approximation problem. Based on the ($p$,$q$)-type resolvent estimate for the fractional Laplacian,…

Analysis of PDEs · Mathematics 2025-09-17 Saumyajit Das , Tuhin Ghosh , Shiqi Ma

We study the theory of scattering for a Schr"odinger equation in an external time dependent magnetic field in the Coulomb gauge, in space dimension 3. The magnetic vector potential is assumed to satisfy decay properties in time that are…

Analysis of PDEs · Mathematics 2007-05-23 J. Ginibre , G. Velo

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…

Mathematical Physics · Physics 2023-04-06 Tuncay Aktosun , Ricardo Weder

We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical…

Statistical Mechanics · Physics 2012-05-08 L. L. Sanchez-Soto , J. J. Monzon , A. G. Barriuso , J. F. Carinena

We develop a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional (chiral) waveguides, for example, with coherent pulsed excitation. The temporal…

Quantum Physics · Physics 2018-05-30 Kevin A. Fischer , Rahul Trivedi , Vinay Ramasesh , Irfan Siddiqi , Jelena Vučković