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Magnetic rings

Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael (2018), Magnetic rings, Journal of Mathematical Physics, 59, 5. 10.1063/1.5022121

Type
Article accepté pour publication ou publié
Date
2018
Journal name
Journal of Mathematical Physics
Volume
59
Number
5
Publisher
American Institute of Physics
Publication identifier
Metadata
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Author(s)
Dolbeault, Jean cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Esteban, Maria J. cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laptev, Ari

Loss, Michael
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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.
Subjects / Keywords
Bohm-Aharonov magnetic potential; magnetic Hardy inequality; magnetic ring; magnetic interpolation inequality; magnetic Schrödinger operator; magnetic Keller-Lieb-Thirring inequality