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Abstract
When a superconducting sample is submitted to a sufficiently strong external magnetic field, the superconductivity of the material is lost. In this paper we prove that this effect does not, in general, take place at a unique value of the external magnetic field strength. Indeed, for a sample in the shape of a narrow annulus the set of magnetic field strengths for which the sample is superconducting is not an interval. This is a rigorous justification of the Little–Parks effect. We also show that the same oscillation effect can happen for discshaped samples if the external magnetic field is nonuniform. In this case the oscillations can even occur repeatedly along arbitrarily large values of the Ginzburg–Landau parameter κ. The analysis is based on an understanding of the underlying spectral theory for a magnetic Schrödinger operator. It is shown that the ground state energy of such an operator is not in general a monotone function of the intensity of the field, even in the limit of strong fields.
Original language  English 

Journal  Communications in Mathematical Physics 
Volume  337 
Issue  1 
Pages (fromto)  191224 
Number of pages  36 
ISSN  00103616 
DOIs  
Publication status  Published  13 Jan 2015 
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Dive into the research topics of 'Lack of Diamagnetism and the Little–Parks Effect'. Together they form a unique fingerprint.Projects
 1 Finished

Semiclassical Quantum Mechanics
Fournais, S. (PI), Madsen, P. (Participant), Mikkelsen, S. (Participant), Miqueu, J.P. C. (Participant) & Bley, G. (Participant)
01/07/2015 → 31/12/2020
Project: Research