Spectral analysis of wave localization and diffusion in random media

Abstract

An original approach to the description of classical wave localization and diffusion in random media is developed. This approach accounts explicitly for the correlation properties of the disorder and is general with respect to the dimensionality of the system. Specifically, we evaluate a two-frequency mutual coherence function, which is an important quantity in itself, and also because the spectral correlator determines the evolution of transient signals in the time domain. The predictions of our theory describe a ballistic to diffusive transition in the wave transport, and, for not too large distances (not exceeding, roughly, several hundreds of mean-free paths) are consistent, in general, with a classical diffusion paradigm. Since the coherence function is expressed via an arbitrary form power spectrum, the results obtained in the work open a new avenue in studying wave transport in anisotropic and/or fractally correlated systems.