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Mixed Normal-Superconducting States in the Presence of Strong Electric Currents

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Abstract

We study the Ginzburg–Landau equations in the presence of large electric currents that are smaller than the critical current where the normal state loses its stability. For steady-state solutions in the large \({\kappa}\) limit, we prove that the superconductivity order parameter is exponentially small in a significant part of the domain, and simply small in the rest of it. Similar results are obtained for the time-dependent problem, in continuation of the paper by the two first authors [3]. We conclude by obtaining some weaker results, albeit similar, for steady-state solutions in the large domain limit.

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Authors and Affiliations

  1. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, USA

    Yaniv Almog

  2. Laboratoire de Mathématiques Jean Leray, CNRS, Université de Nantes, 2 rue de la Houssinière, 44322, Nantes Cedex, France

    Bernard Helffer

  3. Laboratoire de Mathématiques, Université Paris-Sud 11, CNRS, Univ Paris-Saclay, Saint-Aubin, France

    Bernard Helffer

  4. Department of Mathematics, East China Normal University, Shanghai, People’s Republic of China

    Xing-Bin Pan

  5. NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, Shanghai, 200062, People’s Republic of China

    Xing-Bin Pan

Authors
  1. Yaniv Almog
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  2. Bernard Helffer
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  3. Xing-Bin Pan
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Corresponding author

Correspondence to Yaniv Almog.

Additional information

Communicated by S. Serfaty

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Almog, Y., Helffer, B. & Pan, XB. Mixed Normal-Superconducting States in the Presence of Strong Electric Currents. Arch Rational Mech Anal 223, 419–462 (2017). https://doi.org/10.1007/s00205-016-1037-4

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  • DOI: https://doi.org/10.1007/s00205-016-1037-4

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