The Non-Commutative Geometry of the Quantum Hall Effect

Details The Non-Commutative Geometry of the Quantum Hall Effect The Non-Commutative Geometry of the Quantum Hall Effect

1994-11-14

arxiv.org/abs/cond-mat/9411052v1

Physics

Condensed Matter

90 pages, latex, uuencoded file including 6 post-script figures; to uuencode, execute the file; latex will automatically inclu

Scientific paper

10.1063/1.530758

We give an overview of the Integer Quantum Hall Effect. We propose a
mathematical framework using Non-Commutative Geometry as defined by A. Connes.
Within this framework, it is proved that the Hall conductivity is quantized and
that plateaux occur when the Fermi energy varies in a region of localized
states.

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