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Quantum Hall effect and noncommutative geometry

Carey, Alan; Hannabuss, Keith; Mathai, Varghese


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...[Show more]

CollectionsANU Research Publications
Date published: 2006
Type: Journal article
Source: Journal of Geometry and Symmetry in Physics


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