SPATIAL CORRELATIONS OF CHAOTIC WAVE-FUNCTIONS

The statistics of tile spatial correlations of eigenfunctions is inves tigated in chaotic systems with or without time-reversal symmetry. It is rigorously shown that wave functions corresponding to different ene rgy levels are uncorrelated in space. At a given eigenstate, we find t hat though the background of wave function density fluctuates strongly , there exist the long-standing Friedel oscillations in wave function intensity. The joint distribution of the intensity at two separate spa ce points is presented by the universal law with one parameter the ave rage amplitude correlation. This distribution encompasses two differen t regions: One with an independent joint distribution for small values of density fluctuations, and the other showing an increasing spatial correlation for the large fluctuations.