2010/07/08 by François Germinet, Germinet, François, Constanza Rojas-Molina +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1007.1329
8 pages
arxiv created 2010/07/08 · openalex publication_date 2010/07/08 · arxiv updated 2010/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citeGKS. 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.