2003/06/28 by Sandro Graffi, Marco Lenci
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.DS #math.MP #math.SP #msc:37D25 #msc:37D50 #msc:81Q50 #quant-ph
paper · pdf · doi:10.1023/b:joss.0000037218.05161.f3
published as J. Statist. Phys. 116 (2004), no. 1-4, 821-830 · 9 pages
arxiv created 2003/06/28 · openalex publication_date 2004/08/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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)-α, α∈ (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.