Boson peak in various random-matrix models

A so-called boson peak in the reduced density $g(\omega)\omega^2$ of vibrational states is one of the most universal properties of amorphous solids (glasses). It quantifies the excess density of states above the Debye value at low frequencies $\omega$. Its nature is not fully understood and, at a first sight, is nonuniversal. It is shown in this work that, under rather general assumptions, the boson peak emerges in a natural way in very dissimilar models of stable random dynamic matrices possessing translational symmetry. This peak can be shifted toward both higher and lower frequencies (down to zero frequency) by varying the parameters of the distribution and the degree of disorder in the system. The frequency $\omega_b$ of the boson peak appears to be proportional to the elastic modulus $E$ of the system in all cases under investigation.