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).