Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations
Frank R, Hainzl C, Schlein B, Seiringer R. 2016. Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. Letters in Mathematical Physics. 106(7), 913–923.
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Author
Frank, Rupert;
Hainzl, Christian;
Schlein, Benjamin;
Seiringer, RobertISTA 
Department
Grant
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.
Publishing Year
Date Published
2016-07-01
Journal Title
Letters in Mathematical Physics
Publisher
Springer
Acknowledgement
Open access funding provided by Institute of Science and Technology (IST Austria).
Volume
106
Issue
7
Page
913 - 923
IST-REx-ID
Cite this
Frank R, Hainzl C, Schlein B, Seiringer R. Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. Letters in Mathematical Physics. 2016;106(7):913-923. doi:10.1007/s11005-016-0847-5
Frank, R., Hainzl, C., Schlein, B., & Seiringer, R. (2016). Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-016-0847-5
Frank, Rupert, Christian Hainzl, Benjamin Schlein, and Robert Seiringer. “Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations.” Letters in Mathematical Physics. Springer, 2016. https://doi.org/10.1007/s11005-016-0847-5.
R. Frank, C. Hainzl, B. Schlein, and R. Seiringer, “Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations,” Letters in Mathematical Physics, vol. 106, no. 7. Springer, pp. 913–923, 2016.
Frank R, Hainzl C, Schlein B, Seiringer R. 2016. Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. Letters in Mathematical Physics. 106(7), 913–923.
Frank, Rupert, et al. “Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations.” Letters in Mathematical Physics, vol. 106, no. 7, Springer, 2016, pp. 913–23, doi:10.1007/s11005-016-0847-5.
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