Some recent theoretical results on amorphous packings of hard spheres

The aim of this Paper is to review and discuss qualitatively some results Oil the properties of amorphos packings of hard spheres that were recently obtained by means of the replica method. The theory gives predictions for the equation of state of the glass, the complexity of the metastable states, the scaling of the Pressure close to jamming, the coordination of the packing and the pair correlation function in any space dimension d. The predictions compare very well with numerical simulations in d=2,3. The asymptotic predictions for d -> infinity are within the rigorous bounds. The theory can be extended to binary mixtures and to hard-core potentials with,in attractive tail or square well.