Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations Journal Article

Author(s): Frank, Rupert L; Hainzl, Christian; Schlein, Benjamin; Seiringer, Robert
Article Title: Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations
Affiliation IST Austria
Abstract: 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.
Keywords: critical temperature; Quasi-free states; Superconductivity; BCS theory
Journal Title: Letters in Mathematical Physics
Volume: 106
Issue 7
ISSN: 1573-0530
Publisher: Springer  
Date Published: 2016-07-01
Start Page: 913
End Page: 923
Copyright Statement: CC BY 4.0
DOI: 10.1007/s11005-016-0847-5
Notes: 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.
Open access: yes (OA journal)
IST Austria Authors
  1. Robert Seiringer
    123 Seiringer
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