UNIVERSALITIES IN THE SPECTRA OF DISORDERED AND CHAOTIC SYSTEMS

The Wigner-Dyson distribution of level spacings plays a central role in the classification of quantum chaotic systems. However, this description provides no information about the dispersion of the energy levels E(i)(X) in response to an external perturbation. For weakly disordered metallic grains we demonstrate that the response depends on the detailed properties of the system only through mean-level spacing, and a conductance which we define. We derive a nonperturbative expression for the autocorrelator of density-of-states fluctuations for systems taken from both the unitary and orthogonal ensembles, showing that the dependence on these two parameters can be removed by a rescaling. We argue that this description applies quite generally to arbitrary perturbations, and that after rescaling the statistical properties of the random functions, E(i)(X) become universal, dependent only on the Dyson ensemble. We demonstrate that this classification can be generalized to a wider class of systems providing a new characterization of quantum chaos. The analytical results are confirmed by numerical simulation of disordered metallic rings and a chaotic billiard where Aharonov-Bohm flux or a background potential provides the external perturbation.