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We study the semiclassical behaviour of eigenfunctions of quantum systems with ergodic classical limit. By the quantum ergodicity theorem almost all of these eigenfunctions become equidistributed in a weak sense. We give a simple derivation of an upper bound of order vertical bar ln h vertical bar(-1) on the rate of quantum ergodicity if the classical system is ergodic with a certain rate. In addition we obtain a similar bound on transition amplitudes if the classical system is weak mixing. Both results generalise previous ones by Zelditch.
|Translated title of the contribution||Upper bounds on the rate of quantum ergodicity|
|Pages (from-to)||1085 - 1098|
|Number of pages||14|
|Journal||Annales Henri Poincaré|
|Publication status||Published - Oct 2006|
Bibliographical notePublisher: Birkhauser Verlag Ag
Other identifier: IDS number 097MQ
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