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Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations - Zurich Open Repository and Archive


Frank, Rupert L; Hainzl, Christian; Schlein, Benjamin; Seiringer, Robert (2016). Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. Letters in Mathematical Physics, 106(7):913-923.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:May 2016
Deposited On:19 May 2017 13:36
Last Modified:02 Jun 2017 18:12
Publisher:Springer
ISSN:0377-9017
Publisher DOI:https://doi.org/10.1007/s11005-016-0847-5

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