On the Spectral Properties of the Perturbed Landau Hamiltonian

TL;DR

This paper investigates how the spectral properties of the Landau Hamiltonian are affected by localized magnetic and electric field perturbations, focusing on changes in spectral subspaces and Landau level splitting.

Contribution

It provides a detailed analysis of the spectral subspace modifications and Landau level splitting caused by compactly supported perturbations to the Landau Hamiltonian.

Findings

Spectral subspaces are altered by the perturbations.

Landau levels split into multiple spectral components.

The nature of the splitting depends on the perturbation characteristics.

Abstract

The Landau Hamiltonian governing the behavior of a quantum particle in dimension 2 in a constant magnetic field is perturbed by a compactly supported magnetic field and a similar electric field. We describe how the spectral subspaces change and how the Landau levels split under this perturbation.