Spectral asymptotics for pseudodifferential perturbations of the Landau Hamiltonian

Esteban Cárdenas, Pontificia Universidad Católica de Chile

Abstract

In this talk we consider the operator H₀+V, where H₀ is the Landau Hamiltonian and V is a compact pseudodifferential operator. We analyze the asymptotic behavior of the spectrum near the Landau levels and its relation to the symbol of V, which we allow to be of two types. First, we let V have a definite sign and a fast-decaying anti-Wick symbol and, secondly, we consider the case where V has a Weyl symbol with power-like decay. The talk is based on a joint work with Georgi Raikov.