Study of a mobility edge by a new perturbation theory

This is the authors' abstract. We don't add key points for this paper.

The recursion method is applied to the Anderson model of disorder on a Cayley tree, i.e. a Bethe lattice. For small disorder an infinite order perturbation theory is applied which determines the distributions of parameters of a tight-binding linear chain which is exactly equivalent to the original system. The linear chain possesses localized states and extended states separated in energy by mobility edges. Analysis of the linear chain gives the position of the mobility edges, the nature of the singularity at the mobility edge, and the spatial extent of the localized states. A universal property of the Gaussian distribution is demonstrated and comments are made about a Cauchy distribution.