Quantisations of Piecewise Parabolic Maps on the Torus and their Quantum Limits

C-H Chang, T Krüger, RCV Schubert, S Troubetzkoy

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

1 Citation (Scopus)

Abstract

For general quantum systems the semiclassical behaviour of eigenfunctions in relation to the ergodic properties of the underlying classical system is quite difficult to understand. The Wignerfunctions of eigenstates converge weakly to invariant measures of the classical system, the so-called quantum limits, and one would like to understand which invariant measures can occur that way, thereby classifying the semiclassical behaviour of eigenfunctions. We introduce a class of maps on the torus for whose quantisations we can understand the set of quantum limits in great detail. In particular we can construct examples of ergodic maps which have singular ergodic measures as quantum limits, nd examples of non-ergodic maps where aebitary convex combinations of absolutely continuous ergodic measures can occur as quantum limits. The maps we quantise are obtained by cutting and stacking.
Translated title of the contributionQuantisations of Piecewise Parabolic Maps on the Torus and their Quantum Limits
Original languageEnglish
Pages (from-to)395 - 418
Number of pages24
JournalCommunications in Mathematical Physics
Volume282, number 2
DOIs
Publication statusPublished - Sep 2008

Bibliographical note

Publisher: Springer

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