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Breakdown of superconductivity in a magnetic field with self-intersecting zero set

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  • Kamel Attar

    (Lebanese University)

Abstract

We prove that the lowest eigenvalue of the Laplace operator with a magnetic field having a self-intersecting zero set is a monotone function of the parameter defining the strength of the magnetic field, in a neighborhood of infinity. We apply this monotonicity result on the study of the transition from superconducting to normal states for the Ginzburg-Landau model, and prove that the transition occurs at a unique threshold value of the applied magnetic field.

Suggested Citation

  • Kamel Attar, 2021. "Breakdown of superconductivity in a magnetic field with self-intersecting zero set," Partial Differential Equations and Applications, Springer, vol. 2(4), pages 1-14, August.
    • Handle: RePEc:spr:pardea:v:2:y:2021:i:4:d:10.1007_s42985-021-00114-7
    DOI: 10.1007/s42985-021-00114-7
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    Keywords

    35Q56; 35P15; 34L05;
    All these keywords.

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