Signatures of Prelocalized States in Classically Chaotic Systems

We investigate the statistics of eigenfunction intensities ${\cal P}(|\psi|^2)$ in dynamical systems with classical chaotic diffusion. Our results contradict some recent theoretical considerations which challenge the applicability of field theoretical predictions, derived in a different framework for diffusive disordered samples. For two-dimensional systems, the tails of $\mathcal{P}(\mathrm{\mid }\psi {\mathrm{\mid }}^2)$ contradict the results of the optimal fluctuation method, but agree very well with the predictions of the non-linear $\sigma -$model.