Elementary excitations in random substitutional alloys

A theory for elementary excitations in random substitutional alloys with off-diagonal as well as diagonal disorder has been developed using a new technique for configurational averaging introduced by Mookerjee. The theory is valid in both the long- and short-mean-free-path regions, and generates a Green's function which is always analytic. The mathematical formalism is illustrated for the case of electrons in a binary alloy with a tight-binding Hamiltonian. Typical results for the densities of states of one-dimensional chains are shown to compare well with essentially exact numerical calculations.