A Trace Formula for the Eigenvalue Clusters of the Perturbed Landau Hamiltonian

Hamiltonians in Magnetic Fields

20 September 14:00 - 15:00

Georgi Raikov - Pontificia Universidad Católica de Chile

I will discuss a trace formula for the eigenvalue clusters of the Landau Hamiltonian (i.e. the 2D Schroedinger operator with a constant magnetic field), perturbed by an electric potential which decays at infinity. The spectrum of this Hamiltonian consists of clusters of eigenvalues which accumulate to the Landau levels. The asymptotic density of the eigenvalues in these clusters is studied when the cluster number tends to infinity. This asymptotic density is described explicitly in terms of the Radon transform of the perturbation potential. The main tools applied in the proofs of the results, are pseudodifferential operators with contravariant symbols. This is a joint work with A. Pushnitski (King's College, London, UK) and Carlos Villegas-Blas (UNAM, Cuernavaca, Mexico).
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