Veranstaltung

Vortrag
The spectrum of the perturbed Landau Hamiltonian
Prof. Dr. Grigori Rozenblioum (Chalmers University Sweden)
24.4.2006, 14:00 Uhr – 15:00 Uhr

The Landau Hamiltonian describes the quantum behavior of an electron confined to a plane, under the influence of the constant magnetic field. The spectrum of this operator consists of infinitely degenerate eigenvalues, Landau levels. It is natural to expect that under a perturbation of the operator the Landau levels split. This fact was established recently for the case of perturbation by a compactly supported electtric field, and it was found that the perturbed eigenvalues converge to the Landau levels very fact, superexponentially. In the talk we present the newest results concerning a perturbation by a compactly supported MAGNETIC field. We find a rather exact approximation to the new position of spectral subspaces, the latter change rather strongly. The eigenvalues still split superexponentially. We prove an estimate from above for this splitting, and under some additional conditions, the asymptotics of the perturbed eigenvalues.

Verknüpft mit:

• Grigori Rozenblioum