Nonlinear phonon dispersion in disordered solids emerges from a disorder-induced mesoscopic lengthscale that also controls wave attenuation, and both this softening and non-phononic modes contribute substantially to the boson peak in a disorder-strength-dependent way.
Details of this model can be found in [53]
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Nonlinear phonon dispersion in disordered solids and non-Debye vibrational spectra
Nonlinear phonon dispersion in disordered solids emerges from a disorder-induced mesoscopic lengthscale that also controls wave attenuation, and both this softening and non-phononic modes contribute substantially to the boson peak in a disorder-strength-dependent way.