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Abstract
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Starting from the Bardeen–Cooper–Schrieffer (BCS) free energy functional, we derive
the Ginzburg–Landau functional in the presence of a weak homogeneous
magnetic field. We also provide an asymptotic formula for the BCS critical
temperature as a function of the magnetic field. This extends the previous
works of Frank, Hainzl, Seiringer and Solovej (2012; 2016) to the case of
external magnetic fields with nonvanishing magnetic flux through the unit
cell.
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Mathematical Subject Classification
Primary: 35A15, 35Q56, 82D50, 82D55
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Milestones
Received: 18 August 2021
Revised: 7 July 2022
Accepted: 24 October 2022
Published: 29 March 2023
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