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Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations

Letters in Mathematical Physics volume 106, pages 913–923 (2016)Cite this article

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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Authors and Affiliations

  1. Mathematics 253-37, Caltech, Pasadena, CA, 91125, USA

    Rupert L. Frank

  2. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    Christian Hainzl

  3. Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, 8057, Zurich, Switzerland

    Benjamin Schlein

  4. Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400, Klosterneuburg, Austria

    Robert Seiringer

Authors
  1. Rupert L. Frank
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  2. Christian Hainzl
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  3. Benjamin Schlein
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  4. Robert Seiringer
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Correspondence to Robert Seiringer.

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Frank, R.L., Hainzl, C., Schlein, B. et al. Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations. Lett Math Phys 106, 913–923 (2016). https://doi.org/10.1007/s11005-016-0847-5

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  • DOI: https://doi.org/10.1007/s11005-016-0847-5

Mathematics Subject Classification

  • 82D50
  • 46N50

Keywords

  • superconductivity
  • quasi-free states
  • critical temperature
  • BCS theory