Elastic constant dishomogeneity and $Q^2$ dependence of the broadening   of the dynamical structure factor in disordered systems
  We propose an explanation for the quadratic dependence on the momentum $Q$, of the broadening of the acoustic excitation peak recently found in the study of the dynamic structure factor of many real and simulated glasses. We ascribe the observed $Q^2$ law to the spatial fluctuations of the local wavelength of the collective vibrational modes, in turn produced by the dishomegeneity of the inter-particle elastic constants. This explanation is analitically shown to hold for 1-dimensional disordered chains and satisfatorily numerically tested in both 1 and 3 dimensions. 
M.Montagna (Trento), G.Ruocco (L'Aquila), G.Viliani (Trento), R.Di   Leonardo (L'Aquila), R.Dusi (Trento), G.Monaco (L'Aquil...