Annales Henri Poincaré

, Volume 19, Issue 5, pp 1507–1527 | Cite as

Persistence of Translational Symmetry in the BCS Model with Radial Pair Interaction

  • Andreas Deuchert
  • Alissa Geisinger
  • Christian Hainzl
  • Michael Loss
Open Access


We consider the two-dimensional BCS functional with a radial pair interaction. We show that the translational symmetry is not broken in a certain temperature interval below the critical temperature. In the case of vanishing angular momentum, our results carry over to the three-dimensional case.



Open access funding provided by Institute of Science and Technology (IST Austria). The paper was partially supported by the GRK 1838 and the Humboldt foundation. M.L. was partially supported by NSF grant DMS-1600560. Partial financial support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227) is gratefully acknowledged (A.D.). We are grateful for the hospitality at the Department of Mathematics at the University of Tübingen (M.L.) and at the Georgia Tech School of Mathematics (A.G.).


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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Andreas Deuchert
    • 1
  • Alissa Geisinger
    • 2
  • Christian Hainzl
    • 2
  • Michael Loss
    • 3
  1. 1.Institute of Science and Technology Austria (IST Austria)KlosterneuburgAustria
  2. 2.Mathematisches InstitutUniversität TübingenTübingenGermany
  3. 3.School of MathematicsGeorgia TechAtlantaUSA

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