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arXiv · 2104.11007

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

Kamel Attar
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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.

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Kamel Attar. 2021-04-22. Breakdown of superconductivity in a magnetic field with self-intersecting zero set. https://arxiv.org/abs/2104.11007

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