Upper bounds on the rate of quantum ergodicity

Research output: Contribution to journalArticle (Academic Journal)

15 Citations (Scopus)

Abstract

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 contributionUpper bounds on the rate of quantum ergodicity
Original languageEnglish
Pages (from-to)1085 - 1098
Number of pages14
JournalAnnales Henri Poincaré
Volume7 (6)
DOIs
Publication statusPublished - Oct 2006

Bibliographical note

Publisher: Birkhauser Verlag Ag
Other identifier: IDS number 097MQ

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