Correlations of eigenfunctions in disordered systems

Correlations of eigenfunctions, [\psi(k)(r(1))\(2)\psi(l)(r(2))\(2)], in a disordered system are investigated. We derive general formulas expressing these correlation functions in terms of the supermatrix a model. In the particular case of the weak localization regime we find that the correlations of the same eigenfunction are proportional to g(-1) for large distances, while the correlations of two different eigenfunctions cross over from g(-1) behavior for r(1)=r(2) to g(-2) behavior for \r(1)-r(2)\much greater than l, with g and l being the dimensionless conductance and the mean free path, respectively.