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## 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 contribution | Upper bounds on the rate of quantum ergodicity |
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Original language | English |

Pages (from-to) | 1085 - 1098 |

Number of pages | 14 |

Journal | Annales Henri Poincaré |

Volume | 7 (6) |

DOIs | |

Publication status | Published - Oct 2006 |

### Bibliographical note

Publisher: Birkhauser Verlag AgOther identifier: IDS number 097MQ

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