LONG-RANGE CORRELATIONS IN THE WAVE-FUNCTIONS OF CHAOTIC SYSTEMS

We study correlations of the amplitudes of wave functions of a chaotic system at large distances. For this purpose, a joint distribution fun ction of the amplitudes at two distant points in a sample is calculate d analytically using the supersymmetry technique. The result shows tha t although in the limit of the orthogonal and unitary symmetry classes the correlations vanish, they are finite through the entire crossover regime and may be reduced only by localization effects.