We study the diffusion of monochromatic classical waves in a disordered
acoustic medium by scattering theory. In order to avoid artifacts associated
with mathematical point scatterers, we model the randomness by small but finite
insertions. We derive expressions for the configuration-averaged energy flux,
energy density, and intensity for one, two and three dimensional (1D, 2D and
3D) systems with an embedded monochromatic source using the ladder
approximation to the Bethe-Salpeter equation. We study the transition from
ballistic to diffusive wave propagation and obtain results for the
frequency-dependence of the medium properties such as mean free path and
diffusion coefficient as a function of the scattering parameters. We discover
characteristic differences of the diffusion in 2D as compared to the
conventional 3D case, such as an explicit dependence of the energy flux on the
mean free path and quite different expressions for the effective transport
velocity.Comment: 11 pages, 2 figure