Quantum monodromy in prolate ellipsodial billiards

H Waalkens, HR Dullin

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


This is the third in a series of three papers on quantum billiards with elliptic and ellipsoidal boundaries. In the present paper we show that the integrable billiard inside a prolate ellipsoid has an isolated singular point in its bifurcation diagram and, therefore, exhibits classical and quantum monodromy. We derive the monodromy matrix from the requirement of smoothness for the action variables for zero angular momentum. The smoothing procedure is illustrated in terms of energy surfaces in action space including the corresponding smooth frequency map. The spectrum of the quantum billiard is computed numerically and the expected change in the basis of the lattice of quantum states is found. The monodromy is already present in the corresponding two-dimensional billiard map. However, the full three degrees of freedom billiard is considered as the system of greater relevance to physics. Therefore, the monodromy is discussed as a truly three-dimensional effect. (C) 2002 Elsevier Science (USA).
Translated title of the contributionQuantum monodromy in prolate ellipsodial billiards
Original languageEnglish
Pages (from-to)81 - 112
JournalAnnals of Physics
Volume295 (1)
Publication statusPublished - 10 Jan 2001

Bibliographical note

Publisher: Academic Press Inc Elsevier Science
Other identifier: IDS number 516TB

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