Spectral asymptotics for the Iwatsuka Hamiltonian

Pablo Miranda, Universidad de Santiago de Chile

Abstract

In this talk, we consider the two-dimensional operator H = H₀ + V, where H₀ is the Iwatsuka Hamiltonian, that is the Schrödinger operator with a magnetic field that is invariant in one of the spatial variables, and V is a decaying electric potential. We will describe the accumulation rate of the discrete eigenvalues of H in the gaps of its essential spectrum. Afterward, we consider an extension of this problem to the continuous spectrum of H, by the study of the Spectral Shift Function for the pair (H, H₀). To obtain these results it is necessary first to study the band functions of the Iwatsuka Hamiltonian. Then, we will start by showing the asymptotic behavior of the band functions and their dependence on the magnetic field.

This is part of joint works with Nicolas Popoff.