The quasicrystalline approximation and multiple scattering of waves in random media

Abstract

The quasicrystalline approximation (QCA) was first introduced by Lax to break the infinite heirarchy of equations that results in studies of the coherent field in discrete random media. It simply states that the conditional average of a field with the position of one scatterer held fixed is equal to the conditional average with two scatterers held fixed, i.e., 〈ψ〉iji = 〈ψ〉ii. The QCA has met with great success for a range of concentrations from sparse to dense and for long and intermediate wavelengths. In this paper, the QCA is interpreted as a partial resummation of the multiple scattering series that includes only two body correlations and yields the same dispersion equation. Explicit improvements to the QCA are presented that still require only a knowledge of the two body correlation function.