Frequency law of sound damping in glasses below the boson peak
In plain words
At sound frequencies approaching a terahertz, sound in glasses loses energy by scattering off structural irregularities. Whether the damping grows as the fourth power of frequency, as for small random obstacles, or carries an extra logarithmic factor from long-range correlations of the elastic properties, is disputed.
Precise statement
Below the boson-peak frequency $\omega_{\mathrm{BP}}$, scattering by elastic disorder predicts Rayleigh damping $\Gamma \sim \omega^{d+1}$, while simulations of model glasses (Gelin, Tanaka and Lemaitre, Nature Materials 15, 1177, 2016) found $\Gamma \sim -\omega^{d+1}\operatorname{ln}(\omega)$, attributed to long-range spatial correlations of the elastic constants. Determine the asymptotic form of $\Gamma(\omega)$ in $d = 3$ glasses, its dependence on glass stability, its crossover to the Ioffe-Regel limit near $\omega_{\mathrm{BP}}$, and its link to the plateau of thermal conductivity near 10 K.
What would settle it
Inelastic x-ray or ultraviolet Brillouin scattering on one glass over a decade of frequency below $\omega_{\mathrm{BP}}$, with resolution sufficient to separate $\omega^4$ from $\omega^4 \operatorname{ln}(\omega)$, matched to simulations of the same glass at several stabilities.
Status in the literature
Simulations since 2016 report a logarithmic enhancement; no published measurement on a real glass is known to separate the two laws.