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 function of the amplitudes at two distant points in a sample is calculated analytically using the supersymmetry technique. The result shows that 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.