Georgi Raikov (Pontificia Universidad Catolica de Chile):

Title: Eigenvalue asymptotics for quantum Hall effect Hamiltonians

Abstract:

I will consider a class of 2D magnetic quantum Hamiltonians which arise in the mathematical theory of the quantum Hall effect. The unperturbed Hamiltonian is unitarily equivalent to a direct integral of operators with compact resolvents; hence, its spectrum has a band structure. The perturbations considered will be decaying electric potentials of definite sign. I will discuss the asymptotic distribution of the discrete spectrum of the perturbed operator, situated in the open gaps of the essential one. The talk will be based on joint works with Vincent Bruneau (Bordeaux) and Pablo Miranda (Santiago de Chile).