Effects of short-range order on the spectral density function for a one-dimensional amorphous solid

The spectral density A (Q, E) is calculated exactly for a one-dimensional model of an amorphous solid. The model contains an adjustable short-range order parameter α, and A (Q, E) is calculated for serveral values of α. The harmonic-oscillator Hamiltonian appropriate to lattice vibrations and a tight-binding Hamiltonian describing in a simplified way either electrons or spin waves are studied for nearest-neighbor interactions. The calculated spectral densities are compared with the recent neutron-scattering measurements of Mook, Wakabayashi, and Pan