Sharp spectral estimates for the perturbed Landau Hamiltonian with $L^p$ potentials

TL;DR

This paper provides precise spectral estimates for the Landau Hamiltonian with $L^p$ potentials, including new results in three dimensions and generalizations to higher dimensions, advancing understanding of spectral cluster behavior.

Contribution

It introduces sharp spectral cluster estimates in 2D, a limiting absorption principle and unique continuation in 3D, and extends these results to higher dimensions.

Findings

Sharp spectral cluster estimates in 2D

New limiting absorption principle in 3D

Unique continuation theorem in 3D

Abstract

We establish a sharp estimate on the size of the spectral clusters of the Landau Hamiltonian with $L^p$ potentials in two dimensions as the cluster index tends to infinity. In three dimensions, we prove a new limiting absorption principle as well as a unique continuation theorem. The results generalize to higher dimensions.