The fixed angle scattering problem with a first order perturbation

We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely determined by \(2n\) measurements up to a natural gauge. We also show that...

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Bibliographic Details
Published inarXiv.org
Main Authors Meroño, Cristóbal J, Potenciano-Machado, Leyter, Salo, Mikko
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.09.2020
Subjects
Gauge invariance
Inverse scattering
Mathematics - Analysis of PDEs
Mathematics - Mathematical Physics
Perturbation
Physics - Mathematical Physics
Plane waves
Wave equations
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Summary:We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely determined by \(2n\) measurements up to a natural gauge. We also show that one can recover the full first order term for a related equation having no gauge invariance, and that it is possible to reduce the number of measurements if the coefficients have certain symmetries. This work extends the fixed angle scattering results of Rakesh and M. Salo to Hamiltonians with first order perturbations, and it is based on wave equation methods and Carleman estimates.
ISSN:2331-8422
DOI:10.48550/arxiv.2009.13315