Spectral density functions for disordered systems

Abstract

This work describes a Monte Carlo calculation of the spectral density function A(k,E) for a one-dimensional model of an amorphous solid. The model contains an adjustable short-range order parameter and A(k,E) is obtained for several values of that parameter. The Hamiltonians considered are: (1) the Hamiltonian describing an electron moving in a potential consisting of randomly placed delta functions, (2) the Hamiltonian describing a system of coupled harmonic oscillators, and (3) a tight-binding Hamiltonian describing in a simplified way either electrons or spin-waves. This numerical calculation was used to interpret recent neutron scattering data on amorphous systems. The spectral density A(k,E) gives the single-particle contribution to the dynamic form factor of neutron scattering theory. In another application of the model calculation, the spectral density is obtained in the quasicrystalline approximation (QCA) for the problem of an electron in a one-dimensional liquid metal. The QCA and exact spectral densities are compared and it is shown that the QCA fails in the strong scattering regime. 14 figures. (DLC)