Analytic properties of the coherent potential approximation and of its molecular generalizations

Abstract

Some analytic properties of the coherent potential approximation (CPA) are derived. As shown recently by Muller-Hartmann (1973), the CPA is analytic: this result is rederived by using a slightly different method. It is then shown that the conditional densities of states are always positive and that the iteration scheme, starting from the averaged t-matrix approximation, is always convergent to the CPA. Finally all these results are extended to the molecular CPA first proposed by Tsukada (1969).