Frank, Rupert L. and Hainzl, Christian and Langmann, Edwin (2019) The BCS critical temperature in a weak homogeneous magnetic field. Journal of Spectral Theory, 9 (3). pp. 1005-1062. ISSN 1664-039X. doi:10.4171/JST/270. https://resolver.caltech.edu/CaltechAUTHORS:20180604-112611120
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Abstract
We show that, within a linear approximation of BCS theory, a weak homogeneous magnetic field lowers the critical temperature by an explicit constant times the field strength, up to higher order terms. This provides a rigorous derivation and generalization of results obtained in the physics literature fromWHH theory of the upper critical magnetic field. A new ingredient in our proof is a rigorous phase approximation to control the effects of the magnetic field.
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| Additional Information: | © 2019 European Mathematical Society. Received June 18, 2017. We are very grateful to Michael Loss, whose ideas played a crucial role in finding the proof of Lemma 29. E. L. would like to thank Yaron Kadem for helpful discussions. The authors would also like to thank an anonymous referee for carefully reading the paper and several remarks that helped us to improve the paper. Partial support by the U.S. National Science Foundation through grant DMS-1363432 (R.L.F.) and by Vetenskapsrådet through grant 2016-05167 (E.L.) is acknowledged. | |||||||||
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| Subject Keywords: | Superconductivity, BCS theory, magnetic field | |||||||||
| Issue or Number: | 3 | |||||||||
| Classification Code: | Mathematics Subject Classification (2010). Primary: 46N50; Secondary: 35Q56, 81Q10, 81Q20, 82D55 | |||||||||
| DOI: | 10.4171/JST/270 | |||||||||
| Record Number: | CaltechAUTHORS:20180604-112611120 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180604-112611120 | |||||||||
| Official Citation: | Frank Rupert, Hainzl Christian, Langmann Edwin: The BCS critical temperature in a weak homogeneous magnetic field. J. Spectr. Theory 9 (2019), 1005-1062. doi: 10.4171/JST/270 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 86788 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 04 Jun 2018 18:42 | |||||||||
| Last Modified: | 15 Nov 2021 20:42 |
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