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Superconductivity Near the Normal State Under the Action of Electric Currents and Induced Magnetic Fields in \({\mathbb{R}^2}\)

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Abstract

We consider the linearization of the time-dependent Ginzburg-Landau system near the normal state. We assume that an electric current is applied through the sample, which captures the whole plane, inducing thereby, a magnetic field. We show that independently of the current, the normal state is always stable. Using Fourier analysis the detailed behaviour of solutions is obtained as well. Relying on semi-group theory we then obtain the spectral properties of the steady-state elliptic operator.

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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, Univ. Paris-Sud et CNRS, Bât 425, 91 405, Orsay Cedex, France

    Bernard Helffer

  3. Department of Mathematics, East China Normal University, Shanghai, 200062, P.R. 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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Correspondence to Yaniv Almog.

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Communicated by P. Constantin

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Almog, Y., Helffer, B. & Pan, XB. Superconductivity Near the Normal State Under the Action of Electric Currents and Induced Magnetic Fields in \({\mathbb{R}^2}\) . Commun. Math. Phys. 300, 147–184 (2010). https://doi.org/10.1007/s00220-010-1111-y

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  • DOI: https://doi.org/10.1007/s00220-010-1111-y

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