Random Quantum Billiards

We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach is formally distinct from that of the familiar Gaussian orthogonal ensemble, there is remarkable agreement in the resulting distributions of level spacings and in the spectral rigidity. We discuss possible applications of this ensemble to the analysis of real data sets.