03-310 Sandro Graffi, Marco Lenci

Localization in infinite billiards: a comparison between quantum and classical ergodicity (28K, LaTeX 2e with AMS macros) Jun 28, 03

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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.

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