The spectral properties of a singularly perturbed self-adjoint Landau Hamiltonian in the plane with a delta-potential supported on a finite curve are studied. After a general discussion of the qualitative spectral properties of the perturbed Landau Hamiltonian and its resolvent, one of our main objectives is a local spectral analysis near the Landau levels.
This talk is based on joint works with P. Exner, M. Holzmann, V. Lotoreichik, and G. Raikov.[-]

In this talk, I will consider a quantum particle interacting with a target. The target is supposed to be localized and the dynamics of the particle is supposed to be generated by a Lindbladian acting on the space of trace class operators. I will discuss scattering theory for such models associated to a Lindblad operator. First, I will consider situations where the incident particle is necessarily scattered off the target, next situations where the particle may be captured by the target. An important ingredient of the analysis consists in studying scattering theory for dissipative operators on Hilbert spaces.
This is joint work with Marco Falconi, Juerg Froehlich and Baptiste Schubnel.[-]