Microscopic derivation of Ginzburg-Landau theory

Frank, Rupert; Hainzl, Christian; Seiringer, Robert; Solovej, Jan

doi:10.1090/S0894-0347-2012-00735-8

Microscopic derivation of Ginzburg-Landau theory
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by Rupert L. Frank, Christian Hainzl, Robert Seiringer and Jan Philip Solovej;

J. Amer. Math. Soc. 25 (2012), 667-713

DOI: https://doi.org/10.1090/S0894-0347-2012-00735-8

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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