Level and eigenfunction statistics in billiards with surface disorder - art. no. 235315

Statistical properties of billiards with diffusive boundary scattering are investigated by means of the supersymmetric cr model in a formulation appro priate for chaotic ballistic systems. We study level statistics, parametric level statistics, and properties of electron wave functions. In the univer sal regime, our results reproduce conclusions of the random matrix theory, while beyond this regime we obtain a variety of system-specific results det ermined by the classical dynamics in the billiard. Most notably, we find th at level correlations do not vanish at arbitrary separation between energy levels, or if measured at arbitrarily large difference of magnetic fields. Saturation of the lever number variance indicates strong rigidity of the sp ectrum. To study spatial correlations of wave-function amplitudes, we reana lyze and refine derivation of the ballistic version of the sigma model. Thi s allows us to obtain a proper matching of universal short-scale correlatio ns with system-specific ones.