 03310 Sandro Graffi, Marco Lenci
 Localization in infinite billiards: a comparison between quantum and classical ergodicity
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Jun 28, 03

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Abstract. Consider the noncompact 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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