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We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…

Differential Geometry · Mathematics 2025-06-11 Eric Schippers , Wolfgang Staubach

Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…

Analysis of PDEs · Mathematics 2022-02-28 Peter C. Gibson

I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent…

Mathematical Physics · Physics 2024-08-27 Avy Soffer

We show how the scattering-into-cones and flux-across-surfaces theorems in Quantum Mechanics have very intuitive pathwise probabilistic versions based on some results by Carlen about large time behaviour of paths of Nelson diffusions. The…

Mathematical Physics · Physics 2009-11-07 Andrea Posilicano , Stefania Ugolini

We study the scattering of particles and quasiparticles in the framework of algebraic quantum field theory. The main novelty is the construction of inclusive scattering matrix related to inclusive cross-sections. The inclusive scattering…

High Energy Physics - Theory · Physics 2022-10-11 Albert Schwarz

The probability of a quantum particle being detected in a given solid angle is determined by the $S$-matrix. The explanation of this fact in time dependent scattering theory is often linked to the quantum flux, since the quantum flux…

Mathematical Physics · Physics 2010-08-20 Detlef Dürr , Martin Kolb , Tilo Moser , Sarah Römer

Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in general spatial dimension $D\geq 1$ when the density of states…

Quantum Physics · Physics 2021-10-20 Yidan Wang , Michael J. Gullans , Xuesen Na , Seth Whitsitt , Alexey V. Gorshkov

A quantum scattering theory is developed for Fock states scattered by two-level systems in the free space. Compared to existing scattering theories that treat incident light semi-classically, the theory fully quantizes the incident light as…

Optics · Physics 2016-09-21 Jingfeng Liu , Ming Zhou , Zongfu Yu

We study the scattering properties of $N$ identical one-dimensional localized $\mathcal{PT}$-symmetric potentials, connected in series as well as in parallel. We derive a general transfer matrix formalism for parallel coupled quantum…

Quantum Physics · Physics 2016-12-09 Yu Jiang

A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear…

Quantum Physics · Physics 2009-11-13 M. S. Hussein , W. Li , S. Wuester

We develop a formalism for the scattering of a particle on the $q$-deformed Euclidean space. We write down $q$-versions of the Lippmann-Schwinger equation. Their iterative solutions for a weak scattering potential lead us to $q$-versions of…

Quantum Physics · Physics 2022-08-12 Hartmut Wachter

I propose a time-symmetric generalization of quantum mechanics that is inspired by scattering theory. The model postulates two interacting quantum states, one traveling forward in time and one backward in time. The interaction is modeled by…

General Physics · Physics 2022-06-13 Mankei Tsang

We give a pedagogical introduction to time-independent scattering theory in one dimension focusing on the basic properties and recent applications of transfer matrices. In particular, we begin surveying some basic notions of potential…

Quantum Physics · Physics 2020-09-23 Ali Mostafazadeh

The equation for the quantum motion of a Brownian particle in a gaseous environment is derived by means of S-matrix theory. This quantum version of the linear Boltzmann equation accounts non-perturbatively for the quantum effects of the…

Quantum Physics · Physics 2007-05-23 Klaus Hornberger

We present a new approach to real-space multiple-scattering theory for molecules and clusters, based on the two-potential (distorted-wave) Lippmann-Schwinger equation formalism. Our approach uses a recently developed form [D. L. Foulis,…

Mathematical Physics · Physics 2008-06-04 D. L. Foulis

Generalized quantum mechanics is used to examine a simple two-particle scattering experiment in which there is a bounded region of closed timelike curves (CTCs) in the experiment's future. The transitional probability is shown to depend on…

High Energy Physics - Theory · Physics 2009-10-30 Seth Rosenberg

We discuss how a standard scattering theory a of multi-particle theory generalises to systems based on Hamiltonians that involve higher-order derivatives in their quantum mechanical formulation. As concrete examples, we consider Hamiltonian…

High Energy Physics - Theory · Physics 2023-12-22 Andreas Fring , Bethan Turner

The optical theorem is a fundamental aspect of quantum scattering theory. Here, we generalize this theorem to the case where the incident scattering state is a superposition of internal states of the collision partners, introducing…

Atomic Physics · Physics 2022-02-07 Devolder Adrien , Tscherbul Timur V. , Brumer Paul

In the quantum mechanics of collision problems we must consider scattering states of the system. For these states, the wave functions do not remain in Hilbert space, but they are expressible in terms of generalized functions of a Gel'fand…

High Energy Physics - Theory · Physics 2009-10-31 Toshiki Shimbori , Tsunehiro Kobayashi

A new approach is described to the evaluation of the S-matrix in three-dimensional atom-diatom reactive quantum scattering theory. The theory is developed based on natural collision coordinates where progress along the reaction coordinate…

Chemical Physics · Physics 2007-05-23 Ashot S. Gevorkyan , Gabriel G. Balint-Kurti , Gunnar Nyman