A theory for the vibrational dynamics in disordered solids [W. Schirmacher, Europhys. Lett. 73, 892 (2006)], based on the random spatial variation of the shear modulus, has been applied to determine the wave vector ($k$) 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.

• Received 24 August 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.025501