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arXiv · 1905.06152

Thin domain limit and counterexamples to strong diamagnetism

Bernard Helffer·Ayman Kachmar
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Abstract

We study the magnetic Laplacian and the Ginzburg-Landau functional in a thin planar, smooth, tubular domain and with a uniform applied magnetic field. We provide counterexamples to strong diamagnetism, and as a consequence, we prove that the transition from the superconducting to the normal state is non-monotone. In some non-linear regime, we determine the structure of the order parameter and compute the super-current along the boundary of the sample. Our results are in agreement with what was observed in the Little-Parks experiment, for a thin cylindrical sample.

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Bernard Helffer, Ayman Kachmar. 2019-05-15. Thin domain limit and counterexamples to strong diamagnetism. https://doi.org/10.1142/s0129055x215000386

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