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Simon Becker: Metal-insulator transitions in discrete random Schrödinger operators

Time: Thu 2019-04-18 15.30 - 16.30

Location: Seminar Hall Kuskvillan, Institut Mittag-Leffler

Participating: Simon Becker, University of Cambridge

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We study discrete magnetic random Schrödinger operators on the square and honeycomb lattice, both with Anderson-type potentials in weak magnetic fields under weak disorder. We show that there is, in the case of the honeycomb lattice, both strong dynamical localization and delocalization occurring close to the conical point. We prove similar results for the corresponding operator on the Z2-lattice close to the bottom and top of its spectrum. As part of this analysis, we give a rigorous derivation of the quantum hall effect for both models derived from the density of states for which we obtain an asymptotic expansion in the disorder parameter.