Применение теории случайных матриц для описания бозонного пика в двумерных системах

The random matrix theory is applied to describe the vibrational properties of two-dimensional disordered systems with a large number of degrees of freedom. It is shown that the most significant mechanical properties of amorphous solids can be taken into account using the correlated Wishart ensemble. In this ensemble, an excess vibrational density of states over the Debye law is observed as a peak in the reduced density of states g(ω)/ω. Such a peak is known as the boson peak, which was observed in many experiments and numerical simulations for two-dimensional and three-dimensional disordered systems. It is shown that two-dimensional systems have a number of differences in the asymptotic behavior of the boson peak.