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Résumés > Thomas Ourmières-Bonafos- "On the bound states of Schrödinger operators with delta-interactions on conical surfaces" Hamiltonians in strong homogeneous magnetic fields or photonics crystals with high-contrast are approximated by Schrödinger operators with delta-type interactions supported on sets of zero Lebesgue measure (points, curves, surfaces or hypersurfaces). In quantum mechanics, the spectrum of such Schrödinger operators is related to admissible values of the energy and a natural issue is to understand how the geometry of the support of the delta-interaction influences the spectrum. In this talk we consider, in dimension greater than or equal to three, a Laplacian coupled with an attractive delta-interaction supported on a cone whose cross section is the sphere of co-dimension two. We prove that there is discrete spectrum only in dimension three and that, in this case, the eigenvalues are non-decreasing functions of the aperture of the cone. The main result of this work is the exhibition of the precise logarithmic accumulation of the discrete spectrum below the Joint work with Vladimir Lotoreichik |
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