Analytic (unitarity-preserving) approximation for the electronic structure of amorphous systems

Several theories which claim to describe the electronic structure of amorphous systems yield unphysical results such as negative density of states. In this report I present (i) a self-consistent theory which preserves the analytic behavior of the Green's function and (ii) preliminary calculations based on this theory which, in contrast to previously discovered analytic approximations, yields reasonable agreement with "exact" results. Extensions of this theory to elementary excitations (magnons, phonons) in amorphous systems is possible.