Universal velocity correlations in disordered and chaotic systems

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Abstract
The response of weakly disordered metallic grains to Aharonov-Bohm flux suggests a rescaling in which statistical correlators become universal. We derive an exact expression for a correlator of level ‘‘velocities,’’ and provide numerical evidence which suggests that the universality extends to a wider class of systems and generalizes to arbitrary perturbations providing a new characterization of quantum chaos. These results are applied to Fermi velocities of complex lattices.