Echo Expansion in the Theory of Alloys

Abstract

We have obtained a systematic expansion for the trace of the Green's function of electrons moving in a disordered alloy. In our expansion, the terms are classified by a path length which, for some models, takes on discrete values. The expansion is strongly convergent for large complex energies, but seems to be surprisingly useful even for nearly real energies. We present numerical calculations of the density of states for a one-dimensional system.