UNIVERSAL SPECTRAL CORRELATIONS IN DIFFUSIVE QUANTUM-SYSTEMS

We have studied numerically several statistical properties of the spec tra of disordered electronic systems under the influence of an Aharono v-Bohm fluxe phi, which acts as a time-reversal symmetry breaking para meter. The distribution of curvatures of the single-electron energy le vels has a modified Lorentz form with different exponents in the Gauss ian orthogonal ensemble (GOE) and the Gaussian unitary ensemble (GUE) regime. It has Gaussian tails in the crossover regime. The typical cur vature is found to vary as E(c)/Delta ln(1/2)[Delta/(E(c) phi(2))] (E( c) is the Thouless energy and Delta the mean level spacing) and to div erge at zero flux. We show that the harmonics of the variation with ph i of single-level quantities (current or curvature) are correlated, in contradiction with the perturbative result. The single-level current correlation function is found to have a logarithmic behavior at low fl ux. The distribution of single-level currents is non-Gaussian in the G OE-GUE transition regime. We find a universal relation between g(d), t he typical slope of the levels, and g(c), the width of the curvature d istribution, as was proposed by Akkermans and Montambaux. We conjectur e the validity of our results for any chaotic quantum system.