Beyond the effective medium: quasi modes in disordered media

Abstract

For wave propagation in disordered media, the intermediate frequency regime is defined as the frequency range where the wavelength is comparable to the scale of the inhomogeneities. While difficult to treat theoretically, the regime is rich in physical phenomena. The focus of this paper is the transport characteristics of the coherent part of the wave energy in the intermediate frequency range. Through a re-formulation of the well-known coherent potential approximation, a new scheme is developed which is capable of identifying the quasi wave modes as well as yielding their dispersion relations. With no adjustable parameter, this scheme is demonstrated to give an excellent quantitative of the experimental data that showed two branches of the acoustic wave in colloidal suspensions. The new approach is used to predict the quasi modes in a random collection of metallic spheres.