Acoustic attenuation in glasses and its relation with the boson peak

Abstract

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 ($Ω_k)$ and width ($Γ_k$), as well as the density of vibrational states ($g(ω)$), in disordered systems. As a result, we give a firm theoretical ground to the ubiquitous $k^2$ dependence of $Γ_k$ observed in glasses. Moreover, we derive a quantitative relation between the excess of the density of states (the boson peak) and $Γ_k$, 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.

To appear on PRL