We study the level spacing statistics $p(s)$ and eigenfunction properties in a billiard with a rough boundary. Quantum effects lead to localization of classical diffusion in the angular momentum space and the Shnirelman peak in $p(s)$ at small s. The ergodic regime with Wigner-Dyson statistics is identified as a function of roughness. Applications to Q spoiling in optical resonators are also discussed.
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Frahm et al. (1997) studied this question.