# Jussi Behrndt: The Landau Hamiltonian with $\delta$-potential supported on a curve

**Time: **
Wed 2019-04-03 13.15

**Lecturer: **
Jussi Behrndt (TU Graz)

**Location: **
Room F11, KTH

Abstract: In this talk the spectral properties of a singularly perturbed self-adjoint Landau Hamiltonian with a \(\delta\)-potential supported on a finite \(C^{1,1}\)-smooth curve are studied.

After a general discussion of the qualitative spectral properties of this operator and its resolvent, one of the main objectives in this lecture is a local spectral analysis near the Landau levels. Under different conditions on the \(\delta\)-perturbation it is shown that the Landau levels turn into eigenvalue clusters, and the accumulation rate of the eigenvalues within these clusters is determined. Furthermore, the use of Landau Hamiltonians with \(\delta\)-perturbations as model operators for more realistic quantum systems is justified by showing that such operators can be approximated in the norm resolvent sense by a family of Landau Hamiltonians with suitably scaled regular potentials.

This talk is based on a joint work with P. Exner, M. Holzmann, and V.

Lotoreichik.