Abstract
We consider the Ginzburg–Landau functional, defined on a two-dimensional simply connected domain with smooth boundary, in the situation when the applied magnetic field is piecewise constant with a jump discontinuity along a smooth curve. In the regime of large Ginzburg–Landau parameter and strong magnetic field, we study the concentration of the minimizing configurations along this discontinuity by computing the energy of the minimizers and their weak limit in the sense of distributions.
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Acknowledgements
We would like to thank Jacob Christiansen for his insightful comments on the manuscript and Virginie Bonnaillie-Noël for the numerical computations and Fig. 5. We would also like to acknowledge the constructive reviews by the anonymous referees, which led to substantial improvements of this manuscript. The research of the second author was partially supported by a grant from the Lebanese University.
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Assaad, W., Kachmar, A. & Persson-Sundqvist, M. The Distribution of Superconductivity Near a Magnetic Barrier. Commun. Math. Phys. 366, 269–332 (2019). https://doi.org/10.1007/s00220-019-03284-z
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DOI: https://doi.org/10.1007/s00220-019-03284-z