On the quantization of Hall currents in presence of disorder

Jean Michel Combes, François Germinet, Peter D. Hislop

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

2 Scopus citations


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 halfplane 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.

Original languageEnglish
Title of host publicationMathematical Physics of Quantum Mechanics
Subtitle of host publicationSelected and Refereed Lectures from QMath9
EditorsJoachim Asch, Alain Joye
Number of pages17
StatePublished - 2006

Publication series

NameLecture Notes in Physics
ISSN (Print)0075-8450

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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