Localization in infinite billiards: a comparison between quantum and classical ergodicity

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dc.creatorGraffi, Sandro
dc.creatorLenci, Marco
dc.date2003-06-28
dc.date.accessioned2026-07-07T04:30:20Z
dc.date.available2026-07-07T04:30:20Z
dc.descriptionConsider the non-compact billiard in the first quandrant bounded by the positive $x$-semiaxis, the positive $y$-semiaxis and the graph of $f(x) = (x+1)^{-α}$, $α\in (1,2]$. Although the Schnirelman Theorem holds, the quantum average of the position $x$ is finite on any eigenstate, while classical ergodicity entails that the classical time average of $x$ is unbounded.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0306075
dc.identifierhttp://arxiv.org/abs/math-ph/0306075
dc.identifierJ. Statist. Phys. 116 (2004), no. 1-4, 821-830
dc.identifierdoi:10.1023/B:JOSS.0000037218.05161.f3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57433
dc.subjectMathematical Physics
dc.subjectDynamical Systems
dc.subjectSpectral Theory
dc.subjectQuantum Physics
dc.subject81Q50, 37D50, 37D25
dc.titleLocalization in infinite billiards: a comparison between quantum and classical ergodicity
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