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Type: Journal article
Title: Quantum hall effect on the hyperbolic plane in the presence of disorder
Author: Carey, A.
Hannabuss, Keith
Mathai, Varghese
Citation: Letters in Mathematical Physics, 1999; 47(3):215-236
Publisher: Kluwer Academic Publishers
Issue Date: 1999
ISSN: 0377-9017
Statement of
A. Carey, K. Hannabus, V. Mathai
Abstract: We study both the continuous model and the discrete model of the quantum Hall effect (QHE) on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper. 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 Comm. Math. Phys. 190 (1998), 629–673, 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.
Rights: © Springer, Part of Springer Science+Business Media
DOI: 10.1023/A:1007589817182
Appears in Collections:Pure Mathematics publications

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