The dynamical structure factor in disordered systems

TL;DR

This paper investigates how the spectral width of the dynamical structure factor in disordered harmonic solids varies with momentum, revealing different regimes based on the density of states at zero energy, supported by numerical simulations.

Contribution

It identifies two regimes of spectral width behavior in disordered solids and compares analytical predictions with large-scale numerical simulations.

Findings

Rayleigh $p^4$ law for zero density of states at zero energy

Linear behavior when disorder induces non-zero density of states

Numerical results agree with analytical models

Abstract

We study the spectral width as a function of the external momentum for the dynamical structure factor of a disordered harmonic solid, considered as a toy model for supercooled liquids and glasses. Both in the context of single-link coherent potential approximation and of a single-defect approximation, two different regimes are clearly identified: if the density of states at zero energy is zero, the Rayleigh $p^4$ law is recovered for small momentum. On the contrary, if the disorder induces a non vanishing density of states at zero energy, a linear behaviour is obtained. The dynamical structure factor is numerically calculated in lattices as large as $96^3$, and satisfactorily agrees with the analytical computations.