Elementary excitations in disordered systems with short-range order

A general theory for elementary excitations in disordered systems with short-range order has been developed. The theory is based on an averaging formalism which is a generalization of an averaging technique introduced by Mookerjee. The theory is valid for excitations in all mean-free-path regions and can be used to generate analytic Green's functions which have the proper translational symmetry. The mathematical formalism is discussed for random alloys and amorphous solids. Illustrative calculations for Markov chains are shown to compare well with essentially exact numerical calculations.