LONG-RANGE SPATIAL CORRELATIONS OF EIGENFUNCTIONS IN QUANTUM DISORDERED-SYSTEMS

This paper is devoted to thr statistics of the quantum eigenfunctions in an ensemble of metallic grains. We focus on moments of inverse part icipation ratio. In the universal limit that corresponds to the infini te conductance of the grains, these moments are self-averaging quantit ies. At targe but finite conductance the moments do fluctuate duc to t he long-range correlations in the eigenfunctions. We evaluate the dist ributions of fluctuations at given conductance and geometry of the gra ins and express them through the spectrum of the diffusion operator in the grain.