Gor'kov and Eliashberg linear-response theory: Rigorous derivation and limits of applicability

A rigorous microscopic calculation of the polarizability of disordered mesoscopic particles within the grand canonical ensemble is given in terms of the supersymmetry method. The phenomenological result of Gor'kov and Eliashberg is confirmed. Thus the underlying assumptions of their method are justified. This encourages application of random matrix theory in the Gor'kov-Eliashberg style to more complicated situations.