Statistical properties of eigenfunctions of chaotic and disordered systems: Random matrix theory, nonlinear sigma models, and microwave cavity experiments

In the limit of very large mean free path, a chaotic (ballistic) system obeys random matrix theory (RMT) and can also be described by the 0-dimensional (0-D) sigma models. With finite disorder, i.e., with finite mean free path and conductance, the system properties deviate from the RMT and can be described by 1-D sigma models. In this pioneering work, we demonstrated the quantitative consistency between the nonlinear sigma model theory and statistics of the chaotic and disordered wave functions generated in microwave cavity experiments, both for disordered and chaotic cavities. We analyzed the disordered/chaotic eigenfunctions in the space of inverse participation ratio (IPR). We showed for the first time that frequency-driven localized-/delocalized path follows a power law in IPR, that the IPR distribution is symmetric for chaotic system and asymmetric for disordered system and that the intensity-intensity auto-correlation has the general feature of Fredel oscillations whose amplitudes decay with the mean free path, as well as many other important results predicted by the above theories. In summary, our microwave experimental results provide, for the first time, the verifications of the most important predictions of the random matrix theory and nonlinear sigma models. These experiments also show a visualization of Anderson metal and Anderson insulator.

Publications

1. Correlations due to localization in quantum eigenfunctions of disordered microwave cavities
   Prabhakar Pradhan and S. Sridhar
   Phys. Rev. Lett. 85, 2360 (2000)
   Link to the journal   /   PDF   /   cond-mat/0003503