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arXiv · 1801.03810

Magnetic rings

Jean Dolbeault·Maria Esteban·Ari Laptev·Michael Loss
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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 Schr{\"o}dinger 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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Jean Dolbeault, Maria Esteban, Ari Laptev, Michael Loss. 2018-01-11. Magnetic rings. https://doi.org/10.1063/1.5022121

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