Weyl's law and quantum ergodicity for maps with divided phase space

J Marklof, S O'Keefe

Research output: Contribution to journalArticle (Academic Journal)peer-review

25 Citations (Scopus)

Abstract

For a general class of unitary quantum maps, whose underlying classical phase space is divided into several invariant domains of positive measure, we establish analogues of Weyl's law for the distribution of eigenphases. If the map has one ergodic component, and is periodic on the remaining domains, we prove the Schnirelman-Zelditch-Colin de Verdiere theorem on the equidistribution of eigenfunctions with respect to the ergodic component of the classical map (quantum ergodicity). We apply our main theorems to quantized linked twist maps on the torus. In the appendix, Zelditch connects these studies to some earlier results on 'pimpled spheres' in the setting of Riemannian manifolds. The common feature is a divided phase space with a periodic component.
Translated title of the contributionWeyl's law and quantum ergodicity for maps with divided phase space
Original languageEnglish
Pages (from-to)277 - 304
Number of pages18
JournalNonlinearity
Volume18 (1)
DOIs
Publication statusPublished - Jan 2005

Bibliographical note

Publisher: IOP Publishing Ltd
Other identifier: IDS Number: 894JQ

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