Magnetic transport due to a translationally invariant potential obstacle

TL;DR

This paper investigates how a translationally invariant potential obstacle affects the spectral properties of a charged particle in a magnetic field, showing conditions under which discrete Landau levels become continuous spectrum.

Contribution

It derives conditions on translationally invariant potentials that cause Landau levels to transform into an absolutely continuous spectrum.

Findings

Landau levels can become absolutely continuous under certain potentials.

Conditions for spectral transition are explicitly derived.

Implications for magnetic transport phenomena.

Abstract

We consider a two-dimensional system in which a charged particle is exposed to a homogeneous magnetic field perpendicular to the plane and a potential that is translationally invariant in one dimension. We derive several conditions on such a perturbation under which the Landau levels change into an absolutely continuous spectrum.