Acoustic attenuation in glasses and its relation with the boson peak

A theory for the vibrational dynamics in disordered solids [W. Schirmacher, Europhys. Lett. {\bf 73}, 892 (2006)], based on the random spatial variation of the shear modulus, has been applied to determine the wavevector ($k$) dependence of the Brillouin peak position ($\Omega_k)$ and width ($\Gamma_k$), as well as the density of vibrational states ($g(\omega)$), in disordered systems. As a result, we give a firm theoretical ground to the ubiquitous $k^2$ dependence of $\Gamma_k$ observed in glasses. Moreover, we derive a quantitative relation between the excess of the density of states (the boson peak) and $\Gamma_k$, two quantities that were not considered related before. The successful comparison of this relation with the outcome of experiments and numerical simulations gives further support to the theory.