Correlations due to localization in quantum eigenfunctions of disordered microwave cavities

Statistical properties of experimental eigenfunctions of quantum chaotic and disordered microwave cavities are shown to demonstrate nonuniversal correlations due to localization. Varying energy E and mean free path l enable us to experimentally tune from localized to delocalized states. Large level-to-level inverse participation ratio ( I2) fluctuations are observed for the disordered billiards, whose distribution is strongly asymmetric about <I2>. The spatial density autocorrelations of eigenfunctions are shown to spatially decay exponentially and the decay lengths are experimentally determined. All the results are quantitatively consistent with calculations based upon nonlinear sigma models.