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Lack of Diamagnetism and the Little–Parks Effect

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Standard

Lack of Diamagnetism and the Little–Parks Effect. / Fournais, Søren; Sundqvist, Mikael Persson.

I: Communications in Mathematical Physics, Bind 337, Nr. 1, 13.01.2015, s. 191-224.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

Harvard

Fournais, S & Sundqvist, MP 2015, 'Lack of Diamagnetism and the Little–Parks Effect', Communications in Mathematical Physics, bind 337, nr. 1, s. 191-224. https://doi.org/10.1007/s00220-014-2267-7

APA

Fournais, S., & Sundqvist, M. P. (2015). Lack of Diamagnetism and the Little–Parks Effect. Communications in Mathematical Physics, 337(1), 191-224. https://doi.org/10.1007/s00220-014-2267-7

CBE

Fournais S, Sundqvist MP. 2015. Lack of Diamagnetism and the Little–Parks Effect. Communications in Mathematical Physics. 337(1):191-224. https://doi.org/10.1007/s00220-014-2267-7

MLA

Fournais, Søren og Mikael Persson Sundqvist. "Lack of Diamagnetism and the Little–Parks Effect". Communications in Mathematical Physics. 2015, 337(1). 191-224. https://doi.org/10.1007/s00220-014-2267-7

Vancouver

Fournais S, Sundqvist MP. Lack of Diamagnetism and the Little–Parks Effect. Communications in Mathematical Physics. 2015 jan 13;337(1):191-224. https://doi.org/10.1007/s00220-014-2267-7

Author

Fournais, Søren ; Sundqvist, Mikael Persson. / Lack of Diamagnetism and the Little–Parks Effect. I: Communications in Mathematical Physics. 2015 ; Bind 337, Nr. 1. s. 191-224.

Bibtex

@article{5925f805bfb9452d8976025afacc0cb4,
title = "Lack of Diamagnetism and the Little–Parks Effect",
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 disc-shaped samples if the external magnetic field is non-uniform. 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 Schr{\"o}dinger 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.",
author = "S{\o}ren Fournais and Sundqvist, {Mikael Persson}",
year = "2015",
month = jan,
day = "13",
doi = "10.1007/s00220-014-2267-7",
language = "English",
volume = "337",
pages = "191--224",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer",
number = "1",

}

RIS

TY - JOUR

T1 - Lack of Diamagnetism and the Little–Parks Effect

AU - Fournais, Søren

AU - Sundqvist, Mikael Persson

PY - 2015/1/13

Y1 - 2015/1/13

N2 - 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 disc-shaped samples if the external magnetic field is non-uniform. 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.

AB - 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 disc-shaped samples if the external magnetic field is non-uniform. 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.

U2 - 10.1007/s00220-014-2267-7

DO - 10.1007/s00220-014-2267-7

M3 - Journal article

AN - SCOPUS:84922380685

VL - 337

SP - 191

EP - 224

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -