Georgi Raikov (Pontificia Universidad Católica de Chile)

Threshold Singularities of the Spectral Shift Function for Geometric Perturbations of a Magnetic Hamiltonian

Abstract:
I will consider the 3D Schrödinger operator Ho with constant magnetic field, and its perturbations H+ (resp., H- ) obtained from Ho by imposing Dirichlet (resp., Neumann) conditions on an appropriate surface. I will introduce the Krein spectral shift function for the operator pairs ( H+;Ho) and (H-;Ho), and will discuss its singularities at the Landau levels which play the role of thresholds in the spectrum of the unperturbed operator Ho.
The talk is based on a joint work with Vincent Bruneau (Bordeaux).
The financial support of the Chilean Science Foundation Fondecyt under grant 1170816 is gratefully acknowledged.