  The temperature dependence of the thermal conductivity of amorphous solids is
markedly different from that of their crystalline counterparts, but exhibits
universal behaviour. Sound attenuation is believed to be related to this
universal behaviour. Recent computer simulations demonstrated that in the
harmonic approximation sound attenuation $\Gamma$ obeys quartic, Rayleigh
scattering scaling for small wavevectors $k$ and quadratic scaling for
wavevectors above the Ioffe-Regel limit. However, simulations and experiments
do not provide a clear picture of what to expect at finite temperatures where
anharmonic effects become relevant. Here we study sound attenuation at finite
temperatures for model glasses of various stability, from unstable glasses that
exhibit rapid aging to glasses whose stability is equal to those created in
laboratory experiments. We find several scaling laws depending on the
temperature and stability of the glass. First, we find the large wavevector
quadratic scaling to be unchanged at all temperatures. Second, we find that at
small wavectors $\Gamma \sim k^{1.5}$ for an aging glass, but $\Gamma \sim k^2$
when the glass does not age on the timescale of the calculation. For our most
stable glass, we find that $\Gamma \sim k^2$ at small wavevectors, then a
crossover to Rayleigh scattering scaling $\Gamma \sim k^4$, followed by another
crossover to the quadratic scaling at large wavevectors. Our computational
observation of this quadratic behavior reconciles simulation, theory and
experiment, and will advance the understanding of the temperature dependence of
thermal conductivity of glasses.
