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On the spectral properties of the perturbed Landau Hamiltonian

Grigori Rozenblioum
Torsdag, 1 december, 2011, at 16:15-17:00, in Aud. G1 (1532-116)
The Landau Hamiltonian describes the electron moving in the plane under the influence of the constant magnetic field orthogonal to the plane. The spectrum of this system is well known and consists of an infinite sequence of eigenvalues (called Landau levels) of infinite multiplicity.

Under a perturbation of this system  these eigenvalues split into clusters, with the only possible limit points being the Landau levels. We discuss the results on the distribution of the eigenvalues in the clusters, in particular, their rate of convergence to the Landau levels, some  older ones for perturbation by an electric field and more recent ones for perturbations of the magnetic field. Interesting analytical questions on the spectrum properties of Toeplitz operators arise. We also discuss the relations of the problem above with the three-dimensional system and some recent generalizations to the case when the Landau Hamiltonian is replaced by some other related magnetic systems.

Kontaktperson: Jacob Schach Møller