Elastic constant dishomogeneity and $Q^2$ dependence of the broadening of the dynamical structure factor in disordered systems

TL;DR

This paper explains the Q^2 broadening of acoustic peaks in disordered systems as due to elastic heterogeneity causing local wavelength fluctuations, supported by analytical and numerical evidence.

Contribution

It introduces a novel explanation linking elastic constant disorder to vibrational broadening, validated through analytical and numerical methods.

Findings

Q^2 dependence explained by elastic heterogeneity

Analytical model for 1D chains matches numerical results

Numerical tests confirm the theory in 1D and 3D systems

Abstract

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.