# Application of the random matrix theory to the boson peak in glasses

## TL;DR

This paper applies random matrix theory to analyze vibrational states in glasses, deriving equations that explain the boson peak and match numerical results, providing insights into the vibrational properties of amorphous materials.

## Contribution

The study introduces a new approach using correlated random matrix theory to derive the vibrational density of states in glasses, accurately modeling the boson peak.

## Key findings

- Vibrational density follows Debye law at low frequencies.
- The boson peak appears as an additional feature at higher frequencies.
- Derived equations match numerical simulations well.

## Abstract

The density of vibrational states $g(\omega)$ of an amorphous system is studied by using the random-matrix theory. Taking into account the most important correlations between elements of the random matrix of the system, equations for the density of vibrational states $g(\omega)$ are obtained. The analysis of these equations shows that in the low-frequency region the vibrational density of states has the Debye behavior $g(\omega) \sim \omega^2$. In the higher frequency region, there is the boson peak as an additional contribution to the density of states. The obtained equations are in a good agreement with the numerical results and allow us to find an exact shape of the boson peak.