Jun 24 – 28, 2024
Institut de Mathématiques de Toulouse
Europe/Paris timezone

Can one hear an obstacle subject to a constant magnetic field?

Jun 28, 2024, 11:30 AM
Institut de Mathématiques de Toulouse

Institut de Mathématiques de Toulouse

Université Paul Sabatier 118, route de Narbonne - Bat. 1R3 31062 Toulouse Cedex 9


Vincent Bruneau


We consider the Schrödinger and Dirac operators with constant magnetic field in dimensions 2 and 3. The aim of this talk is to give an overview of the known results concerning the distribution of the spectrum of these operators when they are perturbed by an obstacle (operator outside a bounded domain). In the absence of a magnetic field, from Weyl's formulas, it is known that at least the volume of the obstacle appears in the asymptotic expansions of the Spectral Shift Function (or the Scattering Phase), but in the presence of a constant magnetic field, the spectral structure is different. Spectral asymptotics involve the logarithmic capacity of the obstacle (or its projected in the direction of the magnetic field). Some of these results are in collaboration with G. Raikov and with P. Miranda.

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