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 topological (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 Green function is available from a given approximate theory. In the effective-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 illustration some numerical calculations are reported for the random hard-sphere approximation: a comparison with other single-site calculations clearly shows the important role played by a proper inclusion of the structural properties and by the internal co?sistency of the theory.