Moment approach to random systems including off-diagonal randomness and short-range order

Abstract

The function of this work is twofold. One is to present exact values for the first ten moments of the density of states for various disordered alloy models (including off-diagonal randomness and short-range order). These may serve as a standard for the comparison of various approximate theories. In particular, it is shown that the truncation in the range of the T matrix or the mass operator often assumed in multiple scattering formalisms can introduce serious errors when there is off-diagonal randomness. Second, the moments are used to generate approximate expressions for the density of states. In particular it is shown how the technique yields a sensitive test for the effective band edges. This is a new use of a rather old technique. The strengths and weaknesses of the approach are discussed.