Universal vibrational properties of disordered systems in terms of the theory of random correlated matrices

It has been shown that a correlated Wishart ensemble can be used to study the general vibrational properties of stable amorphous solids, where the energy is translationally invariant. The vibrational density of states and the dynamic structure factor of the system have been determined using the random matrix theory. The results indicate the existence of the Ioffe–Regel crossover between low-frequency propagating phonons and diffusons at higher frequencies. The presented vibrational density of states demonstrates the boson peak at the frequency close to the Ioffe—Regel crossover.