Quantum Hall Effect on the Hyperbolic Plane in the Presence of Disorder

被引：0
作者：
A. Carey
K. Hannabus
V. Mathai
机构：
[1] University of Adelaide,Department of Mathematics
[2] University of Oxford,Department of Mathematics
来源：
Letters in Mathematical Physics | 1999年 / 47卷
关键词：
Quantum Hall effect; hyperbolic space; C*-algebras; K-theory; cyclic cohomology; Fuchsian groups; Harper operator; gaps in extended states; random potentials; ergodic action.;
D O I：
暂无
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学科分类号：
摘要：
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.
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页码：215 / 236
页数：21
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