Absolute continuity of the spectrum of a Landau Hamiltonian perturbed by a generic periodic potential

TL;DR

This paper proves that the spectrum of a Landau Hamiltonian with a rational flux and a generic periodic potential is purely absolutely continuous, extending understanding of spectral properties under periodic perturbations.

Contribution

It establishes the absolute continuity of the spectrum for a broad class of periodic potentials in a Landau Hamiltonian with rational flux.

Findings

Spectrum is purely absolutely continuous for generic periodic potentials.

Results apply to Landau Hamiltonians with rational magnetic flux.

Advances understanding of spectral behavior under periodic perturbations.

Abstract

Consider $\Gamma$, a non-degenerate lattice in $\R^2$ and a constant magnetic field $B$ with a flux though a cell of $\Gamma$ that is a rational multiple of $2\pi$. We prove that for a generic $\Gamma$-periodic potential $V$, the spectrum of the Landau Hamiltonian with magnetic field $B$ and periodic potential $V$ is purely absolutely continuous.