ON THE CONDUCTIVITY OF TOPOLOGICALLY DISORDERED-SYSTEMS

An exact analysis is presented for the configurationally averaged two- body Green function of a random tight-binding model characterized by t opological (e.g. positional) disorder. A general consistency relation is found between one-body and two-body Green functions, thus providing a unique and consistent way of extracting the contribution of the two -body function to the conductivity, whenever the averaged one-body Gre en function is available from a given approximate theory. In the effec tive-medium approximation the conductivity problem reduces to the sum of a ladder series for the two-body function, or alternatively to the solution of a simple one-dimensional integral equation. For illustrati on some numerical calculations are reported for the random hard-sphere approximation: a comparison with other single-site calculations clear ly shows the important role played by a proper inclusion of the struct ural properties and by the internal consistency of the theory.