Quantum Hall effect and noncommutative geometry
Carey, Alan; Hannabuss, Keith; Mathai, Varghese
Description
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]
dc.contributor.author | Carey, Alan | |
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dc.contributor.author | Hannabuss, Keith | |
dc.contributor.author | Mathai, Varghese | |
dc.date.accessioned | 2015-12-08T22:45:04Z | |
dc.date.available | 2015-12-08T22:45:04Z | |
dc.identifier.issn | 1312-5192 | |
dc.identifier.uri | http://hdl.handle.net/1885/37669 | |
dc.description.abstract | 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 crossed product algebra. We modify the Fredholm modules defined in [4] in order to prove the integrality of the Hall conductance in this case. | |
dc.publisher | Bulgarian Academy of Sciences | |
dc.source | Journal of Geometry and Symmetry in Physics | |
dc.title | Quantum Hall effect and noncommutative geometry | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 6 | |
dc.date.issued | 2006 | |
local.identifier.absfor | 010102 - Algebraic and Differential Geometry | |
local.identifier.ariespublication | u3169606xPUB152 | |
local.type.status | Published Version | |
local.contributor.affiliation | Carey, Alan, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Hannabuss, Keith, University of Oxford | |
local.contributor.affiliation | Mathai, Varghese, University of Adelaide | |
local.contributor.affiliation | Hannabuss, Keith, Balliol College | |
local.bibliographicCitation.startpage | 16 | |
local.bibliographicCitation.lastpage | 37 | |
dc.date.updated | 2015-12-08T10:50:18Z | |
local.identifier.scopusID | 2-s2.0-84863105985 | |
Collections | ANU Research Publications |
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