2015/04/30 by Rupert L. Frank, Christian Hainzl, Benjamin Schlein +1 · 12 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Constant (computer programming) #Invariant (physics) #Mathematical physics #Order (exchange) #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Statistical physics #Thermal #Thermodynamics #cond-mat.quant-gas #cond-mat.supr-con #math-ph #math.MP
paper · pdf · doi:10.1007/s11005-016-0847-5
published in Letters in Mathematical Physics 106(7), 913-923 (Springer Science+Business Media) · to appear in LMP
arxiv created 2016/04/18 · openalex publication_date 2016/05/10 · arxiv updated 2016/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.