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We consider the defocusing, energy subcritical wave equation $\partial_t^2 u - \Delta u = -|u|^{p-1} u$ in dimension $d \in \{3,4,5\}$ and prove the exterior scattering of solutions if $3\leq d \leq 5$ and $1+6/d<p<1+4/(d-2)$. More…

Analysis of PDEs · Mathematics 2020-09-30 Ruipeng Shen

In this paper,we show that spherical bounded energy solution of the defocusing 3D energy critical Schr\"odinger equation with harmonic potential, $(i\partial_t + \frac {\Delta}2+\frac {|x|^2}2)u=|u|^4u$, exits globally and scatters to free…

Analysis of PDEs · Mathematics 2007-05-23 Zhang Xiaoyi

In this work, we study the scattering of a spinless charged particle constrained to move on a curved surface in the presence of the Aharonov-Bohm potential. We begin with the equations of motion for the surface and transverse dynamics…

In this paper, we establish a conformal scattering theory for defocusing semilinear wave equations on Schwarzschild spacetime. We combine the energy and pointwise decay results for solutions obtained in \cite{Yang} with a Sobolev embedding…

Analysis of PDEs · Mathematics 2026-03-20 Pham Truong Xuan

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

A quantum theory of spherically symmetric thin shells of null dust and their gravitational field is studied. In Nucl. Phys. 603 (2001) 515 (hep-th/0007005), it has been shown how superpositions of quantum states with different geometries…

General Relativity and Quantum Cosmology · Physics 2013-05-29 M. Ambrus , P. Hajicek

We theoretically and numerically prove that under an electromagnetic plane wave with linear polarization incident normally to cylindrical passive scatterers, a single energy diagram can integrate absorption, scattering, and extinction cross…

Optics · Physics 2020-12-04 Jeng Yi Lee

Scattering on the energy shell is viewed here as the relation between the bound states of the Hamiltonian, restricted to sections on leads that are asymptotically independent, far away from the interaction region. The decomposition is…

chao-dyn · Physics 2009-10-31 Raul O. Vallejos , Alfredo M. Ozorio de Almeida

For any $n\geq4$ even, we establish a complete scattering theory for the linear wave equation on the $(n+1)$-dimensional de Sitter space. We prove the existence and uniqueness of scattering states, and asymptotic completeness. Moreover, we…

General Relativity and Quantum Cosmology · Physics 2024-05-10 Serban Cicortas

The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an…

Statistical Mechanics · Physics 2009-11-11 Michael J. Caola

Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of…

Mathematical Physics · Physics 2011-03-11 Anton Krynkin , Olga Umnova , Alvin Y. B. Chong , Shahram Taherzadeh , Keith Attenborough

In this paper, we study the solutions to the energy-critical quadratic nonlinear Schr\"odinger system in ${\dot H}^1\times{\dot H}^1$, where the sign of its potential energy can not be determined directly. If the initial data ${\rm u}_0$ is…

Analysis of PDEs · Mathematics 2021-07-13 Chuanwei Gao , Fanfei Meng , Chengbin Xu , Jiqiang Zheng

We study the spherical collapse of non-top-hat matter fluctuations in the presence of dark energy with arbitrary sound speed. The model is described by a system of partial differential equations solved using a pseudo-spectral method with…

Cosmology and Nongalactic Astrophysics · Physics 2023-02-22 R. C. Batista , H. P. de Oliveira , L. R. W. Abramo

The scattering of free particles constrained to move on a cylindrically symmetric curved surface is studied. The nontrivial geometry of the space contributes to the scattering cross section through the kinetic as well as a possible scalar…

High Energy Physics - Theory · Physics 2009-10-30 Ali Mostafazadeh

A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…

Chaotic Dynamics · Physics 2022-10-12 L. E. Reichl , G. Akguc

Leveraging topological properties in the response of electromagnetic systems can greatly enhance their potential. Although the investigation of singularity-based electromagnetics and non-Hermitian electronics has considerably increased in…

Cold atomic clouds are promising platforms for generating correlated photons, but multiple scattering and associated Doppler broadening limit their temporal coherence. Here we demonstrate that cloud geometry provides a powerful means to…

We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flux estimates on the light cone. Then by the characteristic…

Analysis of PDEs · Mathematics 2024-04-23 Changxing Miao , Ruipeng Shen , Tengfei Zhao

We consider a class of biharmonic nonlinear Schr\"odinger equations with a focusing inhomogeneous power-type nonlinearity \[ i\partial_t u -\Delta^2 u+\mu\Delta u +|x|^{-b} |u|^\alpha u=0, \quad \left. u\right|_{t=0}=u_0 \in…

Analysis of PDEs · Mathematics 2022-11-28 Van Duong Dinh , Sahbi Keraani

We show that the solutions of the three-dimensional critical defocusing nonlinear wave equation with Neumann boundary conditions outside a ball and radial initial data scatter. This is to our knowledge the first result of scattering for a…

Analysis of PDEs · Mathematics 2020-04-21 Thomas Duyckaerts , David Lafontaine