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Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations

Frank, Rupert L. and Hainzl, Christian and Schlein, Benjamin and Seiringer, Robert (2016) Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations. Letters in Mathematical Physics, 106 (7). pp. 913-923. ISSN 0377-9017 .

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We study the time-dependent Bogoliubov–de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a time-dependent Ginzburg–Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full non-linear structure of the equations is necessary to understand this behavior.

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Additional Information:© 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Received: 6 November 2015; Revised: 15 April 2016; Accepted: 16 April 2016; Published online: 10 May 2016. Open access funding provided by Institute of Science and Technology (IST Austria). Financial support from the U.S. National Science Foundation through Grants PHY-1347399 and DMS-1363432 (R.L.F.), SwissMAP and SNF Grant Nr. 200021-153621 (B.S.), and the Austrian Science Fund (FWF) project Nr. P 27533-N27 (R.S.) is acknowledged.
Funding AgencyGrant Number
Institute of Science and Technology AustriaUNSPECIFIED
Swiss National Fund (SNF)200021-153621
FWF Der WissenschaftsfondsP 27533-N27
Subject Keywords:superconductivity, quasi-free states, critical temperature, BCS theory
Classification Code:Mathematics Subject Classification: 82D50, 46N50
Record Number:CaltechAUTHORS:20160722-140945826
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Official Citation:Frank, R.L., Hainzl, C., Schlein, B. et al. Lett Math Phys (2016) 106: 913. doi:10.1007/s11005-016-0847-5
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69171
Deposited By: Tony Diaz
Deposited On:25 Jul 2016 21:27
Last Modified:28 Apr 2017 17:48

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