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Title: Stability estimate for the aligned magnetic field in a periodic quantum waveguide from Dirichlet-to-Neumann map

Abstract

In this article, we study the boundary inverse problem of determining the aligned magnetic field appearing in the magnetic Schrödinger equation in a periodic quantum cylindrical waveguide, by knowledge of the Dirichlet-to-Neumann map. We prove a Hölder stability estimate with respect to the Dirichlet-to-Neumann map, by means of the geometrical optics solutions of the magnetic Schrödinger equation.

Authors:
 [1];  [2];  [2]
  1. Aix Marseille Universite, Toulon Universite, CNRS, CPT, Marseille (France)
  2. (Tunisia)
Publication Date:
OSTI Identifier:
22596841
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MAGNETIC FIELDS; MAPS; MATHEMATICAL SOLUTIONS; PERIODICITY; QUANTUM SYSTEMS; SCHROEDINGER EQUATION; STABILITY; WAVEGUIDES

Citation Formats

Mejri, Youssef, E-mail: josef-bizert@hotmail.fr, Dép. des Mathématiques, Faculté des Sciences de Bizerte, 7021 Jarzouna, and Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur, ENIT BP 37, Le Belvedere, 1002 Tunis. Stability estimate for the aligned magnetic field in a periodic quantum waveguide from Dirichlet-to-Neumann map. United States: N. p., 2016. Web. doi:10.1063/1.4953687.
Mejri, Youssef, E-mail: josef-bizert@hotmail.fr, Dép. des Mathématiques, Faculté des Sciences de Bizerte, 7021 Jarzouna, & Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur, ENIT BP 37, Le Belvedere, 1002 Tunis. Stability estimate for the aligned magnetic field in a periodic quantum waveguide from Dirichlet-to-Neumann map. United States. doi:10.1063/1.4953687.
Mejri, Youssef, E-mail: josef-bizert@hotmail.fr, Dép. des Mathématiques, Faculté des Sciences de Bizerte, 7021 Jarzouna, and Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur, ENIT BP 37, Le Belvedere, 1002 Tunis. Wed . "Stability estimate for the aligned magnetic field in a periodic quantum waveguide from Dirichlet-to-Neumann map". United States. doi:10.1063/1.4953687.
@article{osti_22596841,
title = {Stability estimate for the aligned magnetic field in a periodic quantum waveguide from Dirichlet-to-Neumann map},
author = {Mejri, Youssef, E-mail: josef-bizert@hotmail.fr and Dép. des Mathématiques, Faculté des Sciences de Bizerte, 7021 Jarzouna and Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur, ENIT BP 37, Le Belvedere, 1002 Tunis},
abstractNote = {In this article, we study the boundary inverse problem of determining the aligned magnetic field appearing in the magnetic Schrödinger equation in a periodic quantum cylindrical waveguide, by knowledge of the Dirichlet-to-Neumann map. We prove a Hölder stability estimate with respect to the Dirichlet-to-Neumann map, by means of the geometrical optics solutions of the magnetic Schrödinger equation.},
doi = {10.1063/1.4953687},
journal = {Journal of Mathematical Physics},
number = 6,
volume = 57,
place = {United States},
year = {Wed Jun 15 00:00:00 EDT 2016},
month = {Wed Jun 15 00:00:00 EDT 2016}
}