On the regularity of the Hausdorff distance between spectra of perturbed magnetic Hamiltonians

TL;DR

This paper investigates how the spectra of certain magnetic Hamiltonians change continuously with magnetic field strength, establishing Hölder continuity for a broad class of operators, which advances understanding of spectral stability under magnetic perturbations.

Contribution

It demonstrates Hölder continuity of the Hausdorff distance between spectra of magnetic Hamiltonians with respect to magnetic field intensity, extending spectral regularity results to a wide class of operators.

Findings

Hölder continuity of spectral distance with magnetic field strength

Spectral stability results for magnetic elliptic operators

Applicability to operators with long-range magnetic fields

Abstract

We study the regularity properties of the Hausdorff distance between spectra of continuous Harper-like operators. As a special case we obtain H\"{o}lder continuity of this Hausdorff distance with respect to the intensity of the magnetic field for a large class of magnetic elliptic (pseudo)differential operators with long range magnetic fields.