The Non-Commutative Geometry of the Quantum Hall Effect
Condensed Matter
2009-10-22 v1
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/9411052,
title = {The Non-Commutative Geometry of the Quantum Hall Effect},
author = {J. Bellissard and A. van Elst and H. Schulz-Baldes},
journal= {arXiv preprint arXiv:cond-mat/9411052},
year = {2009}
}
Comments
90 pages, latex, uuencoded file including 6 post-script figures; to uuencode, execute the file; latex will automatically include the figures in the dvi-file