Local spectral asymptotics for metric perturbations of the Landau Hamiltonian

TL;DR

This paper studies how the discrete spectrum of the Landau Hamiltonian changes asymptotically near Landau levels when subjected to various types of metric perturbations, including power-like decay, exponential decay, or compact support.

Contribution

It provides new asymptotic analysis of the discrete spectrum for metric perturbations of the Landau Hamiltonian under different decay conditions.

Findings

Asymptotic behavior characterized near Landau levels

Results for perturbations with power-like decay

Results for perturbations with exponential decay

Abstract

We consider metric perturbations of the Landau Hamiltonian. We investigate the asymptotic behaviour of the discrete spectrum of the perturbed operator near the Landau levels, for perturbations with power-like decay, exponential decay or compact support.