Vibrational behaviour of a realistic amorphous-silicon model

The vibrational properties of a high-quality realistic model of amorphous silicon are examined. The longitudinal and transverse dynamical structure factors are calculated, and fitted to a damped harmonic oscillator (DHO) function. The width $\Gamma$ of the best-fit DHO to the longitudinal dynamical structure factor scales approximately as $k^{2}$ for wavevectors $k\lesssim0.55\textrm{\AA}^{-1}$, which is above the Ioffe-Regel crossover frequency separating the propagating and diffusing regimes, occurring at $k=0.38\pm0.03\textrm{\AA}^{-1}$. Using the DHO function as a fitting function for the transverse dynamical structure factor (without theoretical justification), gives a dependence of $\Gamma\propto k^{\alpha}$ with $\alpha\sim2.5$ for wavevectors $k\lesssim0.7\textrm{\AA}^{-1}$. There was no evidence for $\Gamma\propto k^{4}$ behaviour for either polarization.