1. Thin domain limit and counterexamples to strong diamagnetism.
- Author
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Helffer, Bernard and Kachmar, Ayman
- Subjects
- *
DIAMAGNETISM , *SUPERCONDUCTING transitions , *MAGNETIC fields - 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 nonlinear 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. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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