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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Microscopic derivation of Ginzburg-Landau theory
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by Rupert L. Frank, Christian Hainzl, Robert Seiringer and Jan Philip Solovej PDF
J. Amer. Math. Soc. 25 (2012), 667-713

Abstract:

We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof.
References
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Additional Information
  • Rupert L. Frank
  • Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
  • MR Author ID: 728268
  • ORCID: 0000-0001-7973-4688
  • Email: rlfrank@math.princeton.edu
  • Christian Hainzl
  • Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
  • Email: christian.hainzl@uni-tuebingen.de
  • Robert Seiringer
  • Affiliation: Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC H3A 2K6, Canada
  • Email: robert.seiringer@mcgill.ca
  • Jan Philip Solovej
  • Affiliation: Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
  • ORCID: 0000-0002-0244-1497
  • Email: solovej@math.ku.dk
  • Received by editor(s): February 20, 2011
  • Received by editor(s) in revised form: November 14, 2011
  • Published electronically: March 26, 2012
  • Additional Notes: The first author gratefully acknowledges financial support received via U.S. NSF grant PHY-1068285
    The second author gratefully acknowledges financial support received via U.S. NSF grant DMS-0800906
    The third author gratefully acknowledges financial support received via U.S. NSF grant PHY-0845292 and NSERC
    The last author gratefully acknowledges financial support received via a grant from the Danish council for independent research
  • © Copyright 2012 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.
  • Journal: J. Amer. Math. Soc. 25 (2012), 667-713
  • MSC (2010): Primary 35A15, 81Q20, 82D50, 82D55, 35Q56
  • DOI: https://doi.org/10.1090/S0894-0347-2012-00735-8
  • MathSciNet review: 2904570