Квазилокальные Колебания В Аморфных Твердых Телах С Точки Зрения Теории Негауссовых Случайных Матриц

Abstract

The statistical features of quasi-local vibrations of disordered systems are studied within the framework of the model of correlated random matrices. It is shown that the statistics of matrix elements of the dynamical matrix strongly affects the properties of such vibrations. The lowest frequency part of the density of states of quasilocal vibrations is described by the expression ρ_qlv(ω) ∝ ω^n, where the power n is the number of neighboring atoms. However, if the distribution of matrix elements is highly non-Gaussian, an additional dependence ρ_qlv(ω) ∝ ω^γ appears, where the power γ decreases as the degree of non-Gaussianity increases.