Microscopic Derivation of Ginzburg-Landau Theory

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

Microscopic Derivation of Ginzburg-Landau Theory

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

Institut for Matematiske Fag

39 Citationer (Scopus)

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.

Originalsprog	Engelsk
Tidsskrift	Journal of the American Mathematical Society
Vol/bind	25
Udgave nummer	3
Sider (fra-til)	667-713
Antal sider	47
ISSN	0894-0347
Status	Udgivet - 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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AU - Frank, Rupert

AU - Hainzl, Christian

AU - Seiringer, Robert

AU - Solovej, Jan Philip

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N2 - 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.

AB - 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.

M3 - Journal article

SN - 0894-0347

VL - 25

SP - 667

EP - 713

JO - Journal of the American Mathematical Society

JF - Journal of the American Mathematical Society

IS - 3

ER -

Microscopic Derivation of Ginzburg-Landau Theory

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