Absence of a boson peak in anharmonic phonon models with Akhiezer-type damping

In a recent article M. Baggioli and A. Zaccone (Phys. Rev. Lett. {\bf 112}, 145501 (2019)) claimed that an anharmonic damping, leading to a sound attenuation proportional to $ω^2$ (Akhiezer-type damping) would imply a boson peak, i.e.\ a maximum in the vibrational density of states, divided by the frequency squared (reduced density of states). This would apply both to glasses and crystals.Here we show that this is not the case. In a mathematically correct treatment of the model the reduced density of states monotonously decreases, i.e.\ there is no boson peak. We further show that the formula for the would-be boson peak, presented by the authors, corresponds to a very short one-dimensional damped oscillator system. The peaks they show correspond to resonances, which vanish in the thermodynamic limit.

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