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This book is the third in a series of lectures of the S' eminaire
Poincar' e,whichis directed towards a large audience of physicists
and of mathematicians. 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 aspects are covered, with
some historical background. Inspired by the Bourbaki seminar in
mathematics in its organization, hence nicknamed "Bourbaphi", this
Poincar' e Seminar is held twice a year at the Institut Henri
Poincar' ein Paris,with contri- tions prepared in advance. A
particular care is devoted to the pedagogical nature of the
presentation so as to ful?ll the goal of being readable by a large
audience of scientists.
ThisvolumecontainsthesixthsuchSeminar,heldin2004.Itisdevotedtothe
Quantum Hall E?ect. After a historical and general presentation by
Nobel prize Klaus von Klitzing, discoverer of this e?ect, the
volume proceeds with reviews on the mathematics and physics of both
the integer and fractional case, and includes up to date
presentations of the tunneling and metrology experiments related to
the Quantum Hall E?ect. We hopethat the publicationof this
serieswill servethe community of phy- cists and mathematicians at
professional or graduate student level. ' We thank the Commissariat
'al'Energie Atomique (Division des Sciences de laMati'
ere),theCentreNationaldelaRechercheScienti?que(SciencesPhysiqueet
Math' ematiques), and the Daniel Iagolnitzer Foundation for
sponsoring the Se- nar. Special thanks are due to Chantal Delongeas
for the preparation of the m- uscript.
Recent years have shown important and spectacular convergences
between techniques traditionally used in theoretical physics and
methods emerging from modern mathematics (combinatorics,
probability theory, topology, algebraic geometry, etc). These
techniques, and in particular those of low-dimensional statistical
models, are instrumental in improving our understanding of emerging
fields, such as quantum computing and cryptography, complex
systems, and quantum fluids. This book sets these issues into a
larger and more coherent theoretical context than is currently
available. For instance, understanding the key concepts of quantum
entanglement (a measure of information density) necessitates a
thorough knowledge of quantum and topological field theory, and
integrable models. To achieve this goal, the lectures were given by
international leaders in the fields of exactly solvable models in
low dimensional condensed matter and statistical physics.
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