Microscopic Derivation of the Ginzburg-Landau Model

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

Microscopic Derivation of the Ginzburg-Landau Model

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

Department of Mathematical Sciences

Abstract

We present a summary of our recent 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.

Original language	English
Title of host publication	Proceedings of the XVIIth International Congress on Mathematical Physics : Aalborg, Denmark, 6 – 11 August 2012
Editors	Arne Jensen
Place of Publication	Hackensack, NJ
Publisher	World Scientific
Publication date	2014
Pages	575–583
ISBN (Print)	978-981-4449-23-6
ISBN (Electronic)	978-981-4449-25-0
Publication status	Published - 2014

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http://arxiv.org/abs/1209.1080

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Microscopic Derivation of the Ginzburg-Landau Model. / Frank, Rupert; Hainzl, Christian; Seiringer, Robert et al.
Proceedings of the XVIIth International Congress on Mathematical Physics: Aalborg, Denmark, 6 – 11 August 2012. ed. / Arne Jensen. Hackensack, NJ: World Scientific, 2014. p. 575–583.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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AB - We present a summary of our recent 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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Microscopic Derivation of the Ginzburg-Landau Model

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