Spectrum of the magnetic Schrödinger operator on an infinite wedge

Hamiltonians in Magnetic Fields

23 October 15:30 - 16:30

Nicolas Popoff - Université de Bordeaux

In this talk we are interested in the spectrum of the Schrödinger operator with a constant magnetic field on an infinite wedge, more particularly we want to estimate the bottom of the spectrum and the influence of the geometry. The problem reduces to the analysis of a one-parameter family of 2D-magnetic Schrödinger operators with an electric potential on an infinite sector. The behavior of this family depends on the orientation of the magnetic field. We study what happens when the opening angle of the sector is small. The comparison with a 1D-singular Sturm-Liouville operator gives an upper bound for the bottom of the spectrum of the model operator on the wedge. In application, we get an asymptotics in the semi-classical limit for the first eigenvalue of the magnetic laplacian on a bounded 3D-domain with a curved edge. We compare this asymptotics with known results for the regular case.
Rafael D. Benguria
Pontificia Universidad Católica de Chile
Arne Jensen
Aalborg University
Georgi Raikov
Pontificia Universidad Católica de Chile
Grigori Rozenblioum
Chalmers/University of Gothenburg
Jan Philip Solovej
University of Copenhagen