Magnetic rings

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Date
2018
Dewey
Analyse
Sujet
Bohm-Aharonov magnetic potential; magnetic Hardy inequality; magnetic ring; magnetic interpolation inequality; magnetic Schrödinger operator; magnetic Keller-Lieb-Thirring inequality
Journal issue
Journal of Mathematical Physics
Volume
59
Number
5
Publication date
2018
Publisher
American Institute of Physics
DOI
http://dx.doi.org/10.1063/1.5022121
URI
https://basepub.dauphine.fr/handle/123456789/17523
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Author
Dolbeault, Jean
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Esteban, Maria J.
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laptev, Ari
Loss, Michael
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
We study functional and spectral properties of perturbations of the magnetic Laplace operator on the circle. This operator appears when considering the restriction to the unit circle of a two-dimensional Schrödinger operator with the Bohm-Aharonov vector potential. We prove a Hardy-type inequality on the two-dimensional Euclidean space and, on the circle, a sharp interpolation inequality and a sharp Keller-Lieb-Thirring inequality.