Dynamical mobility edge for various random Landau Hamiltonians

TL;DR

This paper reviews recent findings on the integer quantum Hall effect, demonstrating that various random Landau Hamiltonians exhibit a dynamical mobility edge separating localized and conducting states.

Contribution

It highlights the existence of a dynamical mobility edge in different types of random Landau Hamiltonians, extending understanding of localization and transport in quantum Hall systems.

Findings

Landau gaps are filled by unbounded ergodic electric potentials.

Dynamical mobility edges exist in non-ergodic electric potentials.

Random magnetic potentials also exhibit a transition between localization and transport.

Abstract

We review recent results obtained within the framework of the integer quantum Hall effect in the spirit of the work of Germinet, Klein, Schenker in \cite{GKS}. Landau Hamiltonians perturbed by random electric or magnetic perturbations are shown to exhibit a dynamical mobility edge, that is a transition between a regime of dynamical localization and a regime of non trivial transport at a minimal rate. The focus is put on three situations of interest: 1) unbounded ergodic electric potentials, for which Landau gaps are filled; 2) non ergodic electric potentials; 3) random magnetic potentials.