Monte Carlo studies of multiple scattering of waves in one-dimensinnal random media

A numerical study was undertaken for the ensemble average, or coherent, wave in a one-dimensional random medium composed of uncorrelated point scatterers. Average responses as constructed from numerical solutions of the wave equation were compared to the predictions of the quasicrystalline (QCA) and self-consistent theories. As anticipated, the QCA was found to fail whenever the Waterman and Truell criterion was not satisfied, and also in the case of high scatterer density and low scatterer strength where the attenuation was badly predicted by the QCA. The self-consistent coherent potential approximation failed only under extreme conditions of scatterer strength or density. Nonlocality in the self-energy had a recognizable effect on the average response only in the limiting case of infinite scatterer strength.