Spectral edge regularity of magnetic Hamiltonians

TL;DR

This paper investigates the regularity of spectral edges in magnetic Hamiltonians under bounded magnetic field perturbations, establishing Lipschitz regularity in specific cases and extending previous results.

Contribution

It proves Lipschitz regularity of spectral edges for certain magnetic field perturbations and generalizes earlier findings by Nenciu.

Findings

Lipschitz regularity for constant magnetic fields

Lipschitz regularity for slowly varying magnetic fields

Extension of Nenciu's logarithmic regularity result

Abstract

We analyse the spectral edge regularity of a large class of magnetic Hamiltonians when the perturbation is generated by a globally bounded magnetic field. We can prove Lipschitz regularity of spectral edges if the magnetic field perturbation is either constant or slowly variable. We also recover an older result by G. Nenciu who proved Lipschitz regularity up to a logarithmic factor for general globally bounded magnetic field perturbations.