Geodesic
High-energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows
Jakobson, Dmitry1 ; Strohmaier, Alexander2
1 Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montréal QC H3A 2K6, Canada
2 Mathematisches Institut, Universität Bonn, Beringstrasse 1, D-53115 Bonn, Germany
Electronic research announcements of the American Mathematical Society, Tome 12 (2006), pp. 87-94.

Voir la notice de l'article provenant de la source American Mathematical Society

We relate high-energy limits of Laplace-type and Dirac-type operators to frame flows on the corresponding manifolds, and show that the ergodicity of frame flows implies quantum ergodicity in an appropriate sense for those operators. Observables for the corresponding quantum systems are matrix-valued pseudodifferential operators, and therefore the system remains noncommutative in the high-energy limit. We discuss to what extent the space of stationary high-energy states behaves classically.
DOI : 10.1090/S1079-6762-06-00164-8

Jakobson, Dmitry 1 ; Strohmaier, Alexander 2

1 Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montréal QC H3A 2K6, Canada
2 Mathematisches Institut, Universität Bonn, Beringstrasse 1, D-53115 Bonn, Germany 
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Jakobson, Dmitry; Strohmaier, Alexander. High-energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows. Electronic research announcements of the American Mathematical Society, Tome 12 (2006), pp. 87-94. doi : 10.1090/S1079-6762-06-00164-8. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-06-00164-8/

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