UNIVERSAL CORRELATIONS OF COULOMB-BLOCKADE CONDUCTANCE PEAKS AND THE ROTATION SCALING IN QUANTUM DOTS

We show that the parametric correlations of the conductance peak ampli tudes of a chaotic or weakly disordered quantum dot in the Coulomb-blo ckade regime become universal upon an appropriate seating of the param eter. We compute the universal forms of this correlator for both cases of conserved and broken time-reversal symmetry. For a symmetric dot t he correlator is independent of the details in each lead, such as the number of channels and their correlation. We derive a scaling, which w e call the rotation scaling, that can be computed directly from the do t's eigenfunction rotation rate or alternatively from the conductance peak heights and therefore does not require knowledge of the spectrum of the dot. The relation of the rotation scaling to the level velocity scaling is discussed. The exact analytic form of the conductance peak correlator is derived at short distances. We also calculate the unive rsal distributions of the average level width velocity for various val ues of the scaled parameter. The universality is illustrated in an And erson model of a disordered dot.