Self-Consistent Field Approximation for the Frequency Spectrum of a Disordered Chain

Abstract

The frequency spectrum of a disordered one-dimensional chain is calculated using a self-consistent field approximation. By requiring that the phonon scattering amplitudes satisfy a certain requirement of analytic self-consistency, an implicit equation for the phonon self-energy function is obtained. This equation turns out to be exactly soluble, and leads to a spectral function which possesses no singularities and which exhibits a very flat, broad impurity band.