Random matrix approach to the boson peak and Ioffe-Regel criterion in amorphous solids

We show that the correlated Wishart ensemble can be used to study general vibrational properties of stable amorphous solids with translational invariance. Using the random matrix theory, we found the vibrational density of states and the dynamical structure factor. We demonstrate the presence of the Ioffe-Regel crossover between low-frequency propagating phonons and diffusons at higher frequencies. The reduced vibrational density of states shows the boson peak, which frequency is close to the Ioffe-Regel crossover.