Positive Measure Spectrum for Schroedinger Operators with Periodic Magnetic Fields

TL;DR

This paper investigates the spectral properties of Schrödinger operators with periodic magnetic fields in two-dimensional space, demonstrating that the spectrum has positive measure under certain perturbations even without electric potential.

Contribution

It proves that the spectrum of Schrödinger operators with periodic magnetic fields has positive measure when the magnetic field is a perturbation of a constant field, extending understanding without electric potential.

Findings

Spectrum has positive measure under magnetic perturbations.

Positive measure spectrum occurs even without electric potential.

Results apply to irrational magnetic flux scenarios.

Abstract

We study Schroedinger operators with periodic magnetic field in Euclidean 2-space, in the case of irrational magnetic flux. Positive measure Cantor spectrum is generically expected in the presence of an electric potential. We show that, even without electric potential, the spectrum has positive measure if the magnetic field is a perturbation of a constant one.