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Phase-space localization: topological aspects of quantum chaos. (English) Zbl 1050.81538

Summary: We study quantized classically chaotic maps on a toroidal two-diensional phase space. A discrete, topological criterion for phase-space localization is presented. To each eigenfunction an integer is associated, analogous to a quantized Hall conductivity, which when nonzero reflects phase-space delocalization. A model system is studied, and a correspondence between delocalization and chaotic classical dynamics is discussed.

MSC:

81Q50 Quantum chaos
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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