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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

   

 

Microscopic derivation of Ginzburg-Landau theory


Authors: Rupert L. Frank, Christian Hainzl, Robert Seiringer and Jan Philip Solovej
Journal: J. Amer. Math. Soc. 25 (2012), 667-713
MSC (2010): Primary 35A15, 81Q20, 82D50, 82D55, 35Q56
Published electronically: March 26, 2012
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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.


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Additional Information

Rupert L. Frank
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
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
Email: solovej@math.ku.dk

DOI: http://dx.doi.org/10.1090/S0894-0347-2012-00735-8
PII: S 0894-0347(2012)00735-8
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
Article copyright: © Copyright 2012 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.