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.