The non-commutative geometry of the quantum Hall effect

Bellissard J, van Elst A, Schulz-Baldes H (1994)

Publication Type: Journal article

Publication year: 1994

Journal

Journal of Mathematical Physics American Institute of Physics (AIP)

Publisher: American Institute of Physics (AIP)

Book Volume: 35

Pages Range: 5373-5451

URI: http://de.arxiv.org/abs/cond-mat/9411052

DOI: 10.1063/1.530758

Abstract

An overview of the integer quantum Hall effect is given. A mathematical framework using nonommutative geometry as defined by Connes is prepared. 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.

Authors with CRIS profile

Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

Involved external institutions

Georgia Institute of Technology US United States (USA) (US) Université Toulouse III - Paul Sabatier FR France (FR)

How to cite

APA:

Bellissard, J., van Elst, A., & Schulz-Baldes, H. (1994). The non-commutative geometry of the quantum Hall effect. Journal of Mathematical Physics, 35, 5373-5451. https://dx.doi.org/10.1063/1.530758

MLA:

Bellissard, Jean, A. van Elst, and Hermann Schulz-Baldes. "The non-commutative geometry of the quantum Hall effect." Journal of Mathematical Physics 35 (1994): 5373-5451.

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