Quantum Hall Effect on the Hyperbolic Plane in the presence of disorder

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dc.creatorCarey, A.
dc.creatorHannabuss, K.
dc.creatorMathai, V.
dc.date1998-04-27
dc.date.accessioned2026-07-07T05:24:37Z
dc.date.available2026-07-07T05:24:37Z
dc.descriptionWe study both the continuous model and the discrete model of the integer quantum Hall effect on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper [CHMM]. Here we model impurities, that is we consider the effect of a random or almost periodic potential as opposed to just periodic potentials. The Hall conductance is identified as a geometric invariant associated to an algebra of observables, which has plateaus at gaps in extended states of the Hamiltonian. We use the Fredholm modules defined in [CHMM] to prove the integrality of the Hall conductance in this case. We also prove that there are always only a finite number of gaps in extended states of any random discrete Hamiltonian. [CHMM] A. Carey, K. Hannabuss, V. Mathai and P. McCann, Quantum Hall Effect on the Hyperbolic Plane, Communications in Mathematical Physics, 190 vol. 3, (1998) 629-673.
dc.descriptionLaTeX2e, 17 pages
dc.identifierhttps://arxiv.org/abs/math/9804128
dc.identifierhttp://arxiv.org/abs/math/9804128
dc.identifierLetters in Math. Phys. 47 no. 3 (1999) 215-236
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76870
dc.subjectDifferential Geometry
dc.subjectCondensed Matter
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectOperator Algebras
dc.titleQuantum Hall Effect on the Hyperbolic Plane in the presence of disorder
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