Magnetic rings

Abstract : 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.
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Submitted on : Thursday, May 17, 2018 - 6:59:50 PM
Last modification on : Thursday, February 7, 2019 - 3:47:15 PM
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Jean Dolbeault, Maria Esteban, Ari Laptev, Michael Loss. Magnetic rings. Journal of Mathematical Physics, American Institute of Physics (AIP), 2018, 59 (5), pp.051504. ⟨10.1063/1.5022121⟩. ⟨hal-01680917v2⟩

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