Theory of vibration propagation in disordered media

Irregularity can have a significant impact on the vibrational behavior of elastic systems and can effect a broad range of physical properties, ranging from the acoustic scattering cross section of marine structures to the thermal conductivity of semi-conductors. In many instances, the spatial behavior of the modes of the system is fundamentally altered by the irregularity and decays exponentially with distance. This behavior is known as Anderson localization and dynamically generates a new length scale, the localization length ξ. The modeling of such systems can be quite challenging, with numerical simulations often being misleading owing to finite size effects, and analytical methods being highly specialized and inaccessible to the non-expert in many body theory. We present here an approach which has been highly successful in recent years, the self-consistent diagrammatic theory.