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Microscopic derivation of
Ginzburg-Landau theory and the BCS critical temperature shift
in a weak homogeneous magnetic field
Andreas Deuchert, Christian Hainzl and Marcel Oliver Maier |
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Vol. 4 (2023), No. 1, 1–89
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DOI: 10.2140/pmp.2023.4.1
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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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Authors |
| Andreas Deuchert | |
| Institute of Mathematics University of Zurich Zurich Switzerland |
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| Christian Hainzl | |
| Mathematisches Institut der
Universität München München Germany |
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| Marcel Oliver Maier | |
| Mathematisches Institut der
Universität München München Germany |
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| © 2023 MSP (Mathematical Sciences Publishers). |
