Open Access
2006 Quantum Hall Effect and Noncommutative Geometry
Alan L. Carey, Keith C. Hannabuss, Varghese Mathai
J. Geom. Symmetry Phys. 6: 16-37 (2006). DOI: 10.7546/jgsp-6-2006-16-37


We study magnetic Schrödinger operators with random or almost periodic electric potentials on the hyperbolic plane, motivated by the quantum Hall effect (QHE) in which the hyperbolic geometry provides an effective Hamiltonian. In addition we add some refinements to earlier results. We derive an analogue of the Connes-Kubo formula for the Hall conductance via the quantum adiabatic theorem, identifying it as a geometric invariant associated to an algebra of observables that turns out to be a crossed product algebra. We modify the Fredholm modules defined in [4] in order to prove the integrality of the Hall conductance in this case.


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Alan L. Carey. Keith C. Hannabuss. Varghese Mathai. "Quantum Hall Effect and Noncommutative Geometry." J. Geom. Symmetry Phys. 6 16 - 37, 2006.


Published: 2006
First available in Project Euclid: 20 May 2017

zbMATH: 1104.81088
MathSciNet: MR2267772
Digital Object Identifier: 10.7546/jgsp-6-2006-16-37

Rights: Copyright © 2006 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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