Workshop - Champs magnétiques et analyse semi-classique

Mercredi, 20 Mai, 2015 - 10:30 - 11:15
Ayman Kachmar
Université Libanaise, Beyrouth
Periodic Magnetic Schrödinger Operator in Superconductivity

Since the discovery of type II superconductivity by Abrikosov, the distribution of superconductivity near the second critical field is a challenging mathematical problem. In this talk, I will discuss the asymptotic behavior of the Abrikosov energy in a large domain, and the connection between the Abrikosov and Ginzburg-Landau energies. In this discussion, a key role is played by the spectrum of the Schrödinger operator with a constant magnetic field in a lattice. As a matter of application, I will write a new formula for the distribution of superconductivity near the second critical field. I will conclude the talk with a hierarchy of energies: the Abrikosov energy, the bulk energy of superconductivity, and the reference energy for a superconducting surface. Part of these results are obtained jointly with S. Fournais and with B. Helffer.


Due to technical problems with the microphone, the sound of this video may be partially or completely scrambled, we apologize for this.




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