05-7 Jean-Michel Combes, Francois Germinet, Peter Hislop

On the quantization of Hall currents in presence of disorder (309K, .pdf) Jan 6, 05

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Abstract. We review recent results of two of the authors concerning the quantization of Hall currents, in particular a general quantization formula for the difference of edge Hall conductances in semi-infinite samples with and without a confining wall. We then study the case where the Fermi energy is located in a region of localized states and discuss new regularizations. We also sketch the proof of localization for 2D-models with constant magnetic field with random potential located in a half-plane in two different situations: 1) with a zero potential in the other half plane and for energies away from the Landau levels and 2) with a confining potential in the other half plane and on an interval of energies that covers an arbitrary number of Landau levels.

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