Topological aspects of quantum chaos

Quantized classically chaotic maps on a toroidal two‐dimensional phase space are studied. A discrete, topological criterion for phase‐space localization is presented. To each eigenfunction is associated an integer, analogous to a quantized Hall conductivity, which tests the way the eigenfunction exp...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 1992-01, Vol.2 (1), p.125-130
Main Authors: Leboeuf, P., Kurchan, J., Feingold, M., Arovas, D. P.
Format: Article
Language:English
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Summary:Quantized classically chaotic maps on a toroidal two‐dimensional phase space are studied. A discrete, topological criterion for phase‐space localization is presented. To each eigenfunction is associated an integer, analogous to a quantized Hall conductivity, which tests the way the eigenfunction explores the phase space as some boundary conditions are changed. The correspondence between delocalization and chaotic classical dynamics is discussed, as well as the role of degeneracies of the eigenspectrum in the transition from localized to delocalized states. The general results are illustrated with a particular model.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.165915