Microscopic Derivation of Ginzburg-Landau Theory

Creators: Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip

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.

Additional Information

© 2012 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. Received by the editors February 20, 2011 and, in revised form, November 14, 2011. Published electronically: March 26, 2012. 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. Part of this work was carried out at the Erwin Schrödinger Institute for Mathematical Physics in Vienna, Austria, and the authors are grateful for the support and hospitality during their visit. R.S. would also like to thank the Departamento de Fisica at the Pontificia Universidad Catόlica de Chile for their hospitality.

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