Sandro Graffi, Marco Lenci
Localization in infinite billiards: a comparison between quantum and classical ergodicity
(28K, LaTeX 2e with AMS macros)
ABSTRACT. 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.