The Poincar? Seminar is held twice a year at the Institut Henri Poincar? in Paris. The goal of this seminar is to provide up-to-date information about general topics of great interest in physics. Both the theoretical and experimental results are covered, with some historical background. Particular care is devoted to the pedagogical nature of the presentation. This volume is devoted to the quantum Hall effect. After a historical and general presentation by Nobel prize winner Klaus von Klitzing, discoverer of this effect, the volume proceeds with reviews on the mathematics and physics of both the integer and fractional case. It includes up to date presentations of the tunneling and metrology experiments related to the quantum Hall effect. It will serve the community of physicists and mathematicians at professional or graduate student level.
Progress in Mathematical Physics Volume 45
Editors-in-Chief Anne Boutet de Monvel, Université Paris VII Denis Diderot, France Gerald Kaiser, Center for Signals and Waves, Austin, TX, USA
Editorial Board Sir M. Berry, University of Bristol, UK C. Berenstein, University of Maryland, College Park, USA P. Blanchard, University of Bielefeld, Germany A.S. Fokas, University of Cambridge, UK D. Sternheimer, Université de Bourgogne, Dijon, France C. Tracy, University of California, Davis, USA
The Quantum Hall Effect Poincaré Seminar 2004
Benoît Douçot Bertrand Duplantier Vincent Pasquier Vincent Rivasseau Editors
Birkhäuser Verlag Basel • Boston • Berlin
Editors: Benoît Douçot LPTHE CNRS et Universités Paris 6 et 7 Tour 24-14 5e étage 4 place Jussieu F-75252 Paris Cedex 05 e-mail:
[email protected]
Bertrand Duplantier Service de Physi