Autocorrelation function of eigenstates in chaotic and mixed systems

A Backer, RCV Schubert

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

34 Citations (Scopus)

Abstract

We study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits. We obtain an expansion of the autocorrelation function in terms of the correlation distance. For localized states in billiards, like bouncing ball modes or states living on tori, a simple model using only classical input gives good agreement with the exact result. In particular, a prediction for irregular eigenfunctions in mixed systems is derived and tested. For chaotic systems, the expansion of the autocorrelation function can be used to test quantum ergodicity on different length scales.
Translated title of the contributionAutocorrelation function of eigenstates in chaotic and mixed systems
Original languageEnglish
Pages (from-to)539 - 564
JournalJournal of Physics A: Mathematical and General
Volume35 (3)
Publication statusPublished - 25 Jan 2002

Bibliographical note

Publisher: IOP Publishing Ltd
Other identifier: IDS number 523PV

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