Quantum localization in rough billiards

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 for the Q-spoiling in optical resonators are also discussed.