Scattering and Localization Properties of Highly Oscillatory Potentials

DOI10.1002/cpa.21459zbMath1292.34083arXiv1201.3904OpenAlexW2963771222MaRDI QIDQ5746483

Vincent Duchêne, Iva Vukićević, Michael I. Weinstein

Publication date: 18 February 2014

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.3904

zbMATH Keywords

scatteringSchrödinger equationlocalizationhighly oscillatory potentialsdispersive time decay properties

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Scattering theory for PDEs (35P25) General theory of ordinary differential operators (47E05) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (12)

Spectral asymptotics for the Schrödinger operator on the line with spreading and oscillating potentials ⋮ Resonances for random highly oscillatory potentials ⋮ Oscillatory and Localized Perturbations of Periodic Structures and the Bifurcation of Defect Modes ⋮ Topologically protected states in one-dimensional continuous systems and Dirac points ⋮ Resonances for Schrödinger operators on infinite cylinders and other products ⋮ Wavepackets in inhomogeneous periodic media: Effective particle-field dynamics and Berry curvature ⋮ Bound States for Rapidly Oscillatory Schrödinger Operators in Dimension 2 ⋮ Mathematical study of scattering resonances ⋮ Dirac Operators and Domain Walls ⋮ Defect modes for dislocated periodic media ⋮ Characterization of edge states in perturbed honeycomb structures ⋮ Defect Resonances of Truncated Crystal Structures

Cites Work

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• Inverse scattering on the line
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• Transport in the one-dimensional Schrödinger equation
• The spectrum of a self-adjoint differential operator with rapidly oscillating coefficients on the axis
• Scattering Resonances of Microstructures and Homogenization Theory
• Center manifold for nonintegrable nonlinear Schrödinger equations on the line

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