Laboratoire de Physique Théorique
Toulouse - UMR 5152

The spectral function, or imaginary part of the single-particle, ensemble-averaged Green function, is an important quantity to know in random systems since it encodes important information about the density of states, as well as the mean free life-time of plane waves. Alas, there are very few accurate, analytical approximations known in dimensions larger than one and for spatially correlated disorder, as required for, e.g., cold atoms in laser speckle potentials. In this talk, I will first of all present a brief reminder of the most noteworthy properties of the spectral function, and review a few popular approximations. Secondly, I will preset results from a recent collaboration with Martin Trappe (Singapore) and Dominique Delande (Paris) on a semiclassical approximation to the spectral function valid in strong, spatially correlated disorder, and discuss both its merits and limitations in certain interesting cases.