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The vibrational density of states $D(\omega)$ of solids controls theirthermal and transport properties. In crystals, the low-frequency modes areextended phonons distributed in frequency according to Debye's law, $D(\omega)\propto \omega^2$. In amorphous solids, phonons are damped, and at lowfrequency $D(\omega)$ comprises extended modes in excess over Debye'sprediction, leading to the so-called boson peak in $D(\omega)/\omega^2$ at$\omega_{\rm bp}$, and quasi-localized (QLMs) ones. Here we show that bosonpeak and phonon attenuation in the Rayleigh scattering regime are related, assuggested by correlated fluctuating elasticity theory (corr-FET), and thatamorphous materials can be described as homogeneous isotropic elastic mediapunctuated by QLMs acting as elastic heterogeneities. Our numerical resultsresolve the conflict between theoretical approaches attributing amorphoussolids' vibrational anomalies to elastic disorder and localized defects.

Unifying description of the vibrational anomalies of amorphous materials