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

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

2003-06-28

arxiv.org/abs/math-ph/0306075v1

J. Statist. Phys. 116 (2004), no. 1-4, 821-830

Physics

Mathematical Physics

9 pages

Scientific paper

10.1023/B:JOSS.0000037218.05161.

Consider the non-compact billiard in the first quandrant bounded by the positive $x$-semiaxis, the positive $y$-semiaxis and the graph of $f(x) = (x+1)^{-\alpha}$, $\alpha \in (1,2]$. 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.

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