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Type: Journal article
Title: Quantum Hall effect and noncommutative geometry
Author: Carey, A.
Hannabuss, K.
Varghese, M.
Citation: Journal of Geometry and Symmetry in Physics, 2006; 6(1):16-36
Publisher: Bulgarian Academy of Sciences, Institute of Biophysics
Issue Date: 2006
ISSN: 1312-5192
Statement of
Carey, A.; Hannabuss, K.; Mathai, V.
Abstract: We study magnetic Schrodinger 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.
DOI: 10.7546/jgsp-6-2006-16-37
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