Confining quantum particles with a purely magnetic field

Yves Colin de Verdière[1]; Françoise Truc[2]

  • [1] Institut Fourier UMR 5582 CNRS-UJF BP 74 38402 Saint Martin d’Hères Cedex (France)
  • [2] Unité mixte de recherche CNRS-UJF 5582 Institut Fourier BP 74, 38402-Saint Martin d’Hères Cedex (France)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 7, page 2333-2356
  • ISSN: 0373-0956

Abstract

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We consider a Schrödinger operator with a magnetic field (and no electric field) on a domain in the Euclidean space with a compact boundary. We give sufficient conditions on the behaviour of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magnetic field. We construct examples in the case where the boundary is smooth as well as for polytopes; These examples are highly simplified models of what is done for nuclear fusion in tokamacs. We also present some open problems.

How to cite

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Colin de Verdière, Yves, and Truc, Françoise. "Confining quantum particles with a purely magnetic field." Annales de l’institut Fourier 60.7 (2010): 2333-2356. <http://eudml.org/doc/116336>.

@article{ColindeVerdière2010,
abstract = {We consider a Schrödinger operator with a magnetic field (and no electric field) on a domain in the Euclidean space with a compact boundary. We give sufficient conditions on the behaviour of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magnetic field. We construct examples in the case where the boundary is smooth as well as for polytopes; These examples are highly simplified models of what is done for nuclear fusion in tokamacs. We also present some open problems.},
affiliation = {Institut Fourier UMR 5582 CNRS-UJF BP 74 38402 Saint Martin d’Hères Cedex (France); Unité mixte de recherche CNRS-UJF 5582 Institut Fourier BP 74, 38402-Saint Martin d’Hères Cedex (France)},
author = {Colin de Verdière, Yves, Truc, Françoise},
journal = {Annales de l’institut Fourier},
keywords = {Magnetic field; Schrödinger operator; self-adjointness; magnetic field},
language = {eng},
number = {7},
pages = {2333-2356},
publisher = {Association des Annales de l’institut Fourier},
title = {Confining quantum particles with a purely magnetic field},
url = {http://eudml.org/doc/116336},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Colin de Verdière, Yves
AU - Truc, Françoise
TI - Confining quantum particles with a purely magnetic field
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 7
SP - 2333
EP - 2356
AB - We consider a Schrödinger operator with a magnetic field (and no electric field) on a domain in the Euclidean space with a compact boundary. We give sufficient conditions on the behaviour of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magnetic field. We construct examples in the case where the boundary is smooth as well as for polytopes; These examples are highly simplified models of what is done for nuclear fusion in tokamacs. We also present some open problems.
LA - eng
KW - Magnetic field; Schrödinger operator; self-adjointness; magnetic field
UR - http://eudml.org/doc/116336
ER -

References

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