The blue from the sky: Rayleigh scattering, long-time tails and other spectral anomalies of disordered systems
Prof. W. Schirmacher (Institut fuer Physik, Universitaet Mainz und Physik-Department E13, TU Muenchen)

Rayleigh scattering, which is the origin of the blue color of the sky, does not only arise due to the presence of “scattering particles” but also due to any inhomogeneity in the wave-carrying medium, as pointed out already by Rayleigh himself. So Rayleigh scattering is the dominant long-wavelength scattering mechanism for waves in a statically (”quenched”) disordered system.
Exploiting the mathematical analogy between single-particle diffusion and waves (both obey a Helmholtz equation in frequency space) it will be shown that the ”long-time tail” in the velocity autocorrelation function of single-particle motion in a glass (e.g. in a lithium battery) has the same reason.
Another anomaly in wave motion in disordered systems, the ”boson peak” will be shown to have its diffusive analogy in a transition from normal diffusion to anomalous diffusion. The bosonpeak anomaly arises from ”level repulsion” caused by the disorder-induced local violation of the translational and rotational symmetry .
A field-theoretical treatment of these anomalies, which is in good agreement with measured spectra will be given.