Quantum Hall Effect and Noncommutative Geometry

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dc.creatorCarey, A.
dc.creatorHannabuss, K.
dc.creatorMathai, V.
dc.date2000-08-16
dc.date2005-12-15
dc.date.accessioned2026-07-07T06:35:21Z
dc.date.available2026-07-07T06:35:21Z
dc.descriptionWe study magnetic Schrodinger operators with random or almost periodic electric potentials on the hyperbolic plane, motivated by the quantum Hall effect 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 [CHMM] in order to prove the integrality of the Hall conductance in this case.
dc.description18 pages, paper rewritten
dc.identifierhttps://arxiv.org/abs/math/0008115
dc.identifierhttp://arxiv.org/abs/math/0008115
dc.identifierJournal of Geometry and Symmetry in Physics, vol 6 (2006) 16-37
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99768
dc.subjectOperator Algebras
dc.titleQuantum Hall Effect and Noncommutative Geometry
dc.typetext

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