article published yes Rupert Frank author Christian Hainzl author Benjamin Schlein author Robert Seiringer author 4AFD0470-F248-11E8-B48F-1D18A9856A870000-0002-6781-0521 RoSe department Structure of the Excitation Spectrum for Many-Body Quantum Systems project IST Austria Open Access Fund project 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. https://research-explorer.ista.ac.at/download/1422/5181/IST-2016-591-v1+1_s11005-016-0847-5.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Springer2016 eng 00037884470000210.1007/s11005-016-0847-5 1067913 - 923 Frank, Rupert, et al. “Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations.” <i>Letters in Mathematical Physics</i>, vol. 106, no. 7, Springer, 2016, pp. 913–23, doi:<a href="https://doi.org/10.1007/s11005-016-0847-5">10.1007/s11005-016-0847-5</a>. Frank, Rupert, Christian Hainzl, Benjamin Schlein, and Robert Seiringer. “Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations.” <i>Letters in Mathematical Physics</i>. Springer, 2016. <a href="https://doi.org/10.1007/s11005-016-0847-5">https://doi.org/10.1007/s11005-016-0847-5</a>. 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. R. Frank, C. Hainzl, B. Schlein, and R. Seiringer, “Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations,” <i>Letters in Mathematical Physics</i>, vol. 106, no. 7. Springer, pp. 913–923, 2016. Frank, R., Hainzl, C., Schlein, B., &#38; Seiringer, R. (2016). Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. <i>Letters in Mathematical Physics</i>. Springer. <a href="https://doi.org/10.1007/s11005-016-0847-5">https://doi.org/10.1007/s11005-016-0847-5</a> Frank R, Hainzl C, Schlein B, Seiringer R. Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. <i>Letters in Mathematical Physics</i>. 2016;106(7):913-923. doi:<a href="https://doi.org/10.1007/s11005-016-0847-5">10.1007/s11005-016-0847-5</a> R. Frank, C. Hainzl, B. Schlein, R. Seiringer, Letters in Mathematical Physics 106 (2016) 913–923. 14222018-12-11T11:51:56Z2025-09-18T14:20:53Z