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

Jaroslav Fabian

paper

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

arXiv:cond-mat/0104464

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.

4 pages