# 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:

- Aix Marseille Universite, Toulon Universite, CNRS, CPT, Marseille (France)
- (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}

}

DOI: 10.1063/1.4953687

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