Noncommutative Geometry and Quantum Hall Effect

1995 ◽  
pp. 1238-1246 ◽  
Author(s):  
Jean Bellissard
Keyword(s):  
Hall Effect ◽  
Noncommutative Geometry ◽  
Quantum Hall Effect ◽  
Quantum Hall

scholarly journals The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects

2020 ◽  
Author(s):  
Giuseppe De Nittis ◽  
◽  
Maximiliano Sandoval ◽  
◽  
◽  
...  
Keyword(s):  
Dirac Operator ◽  
Hall Effect ◽  
Noncommutative Geometry ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Spectral Triple ◽  
C Algebra ◽  
Compact Resolvent ◽  
Landau Hamiltonian ◽  
The Continuum

This work provides a first step towards the construction of a noncommutative geometry for the quantum Hall effect in the continuum. Taking inspiration from the ideas developed by Bellissard during the 80's we build a spectral triple for the C∗-algebra of continuous magnetic operators based on a Dirac operator with compact resolvent. The metric aspects of this spectral triple are studied, and an important piece of Bellissard's theory (the so-called first Connes' formula) is proved.

scholarly journals The noncommutative geometry of the quantum Hall effect

1994 ◽  
Vol 35 (10) ◽  
pp. 5373-5451 ◽  
Author(s):  
J. Bellissard ◽  
A. van Elst ◽  
H. Schulz‐ Baldes
Keyword(s):  
Hall Effect ◽  
Noncommutative Geometry ◽  
Quantum Hall Effect ◽  
Quantum Hall

Localization and many-body interactions in the quantum Hall effect determined by polarized optical emission

1991 ◽  
Vol 44 (8) ◽  
pp. 4006-4009 ◽  
Author(s):  
B. B. Goldberg ◽  
D. Heiman ◽  
M. Dahl ◽  
A. Pinczuk ◽  
L. Pfeiffer ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Optical Emission ◽  
Many Body ◽  
Many Body Interactions

Quantum Hall effect in a saddle-point system

1998 ◽  
Vol 2 (1-4) ◽  
pp. 523-526
Author(s):  
M.V Budantsev ◽  
Z.D Kvon ◽  
A.G Pogosov ◽  
E.B Olshanetskii ◽  
D.K Maude ◽  
...  
Keyword(s):  
Saddle Point ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Point System ◽  
Saddle Point System
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