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

Frank, Rupert L and Hainzl, Christian and Schlein, Benjamin and Seiringer, Robert (2016) Incompatibility of time-dependent Bogoliubov–de-Gennesde-Gennes and Ginzburg–Landau equations. Letters in Mathematical Physics, 1 (11). ISSN 1573-0530

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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.

Item Type: Article
DOI: 10.1007/s11005-016-0847-5
Uncontrolled Keywords: critical temperature, Quasi-free states, Superconductivity, BCS theory
Subjects: 500 Science > 510 Mathematics
500 Science > 530 Physics
Research Group: Seiringer Group
SWORD Depositor: Sword Import User
Depositing User: Sword Import User
Date Deposited: 25 May 2016 14:43
Last Modified: 04 Sep 2017 14:52
URI: https://repository.ist.ac.at/id/eprint/591

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