Spectral fluctuations of the atomic vibrations in glasses: random matrix theory and beyond

Abstract

It is demonstrated on a realistic model of amorphous alloy Si$_{0.9}$Ge$_{0.1}$ with 1000 atoms, that short-range spectral fluctuations of propagons and diffusons are universal and in agreement with random matrix theory. The universality ceases at distances greater than Thouless number $N_T$, where propagons obey the Altshuler-Shklovskii power law, $Σ_2\sim N^{3/2}$ for the variance $Σ_2$ of the number of levels $N$, while a new power law, $Σ_2\sim N$, is observed for diffusons.