Brillouin and Boson peaks in Glasses from vector Euclidean Random Matrix Theory

TL;DR

This paper extends Euclidean Random Matrix Theory to vector vibrations in disordered systems, analytically studying Brillouin and Boson peaks, revealing a mechanical instability transition and detailed scaling laws for vibrational properties.

Contribution

It introduces a vector vibration model within ERMT, providing analytical predictions and numerical confirmation of vibrational features and phase transition behaviors in glasses.

Findings

Brillouin peaks exhibit sound-like behavior with distinguishable longitudinal/transverse character at small momentum.

A mechanical instability transition occurs at low densities, with confirmed scaling laws.

Brillouin peaks persist into the unstable phase, mainly affecting linewidths.

Abstract

A simple model of harmonic vibrations in topologically disordered systems, such as glasses and supercooled liquids, is studied analytically by extending Euclidean Random Matrix Theory to include vector vibrations. Rather generally, it is found that i) the dynamic structure factor shows sound-like Brillouin peaks whose longitudinal/transverse character can only be distinguished for small transferred momentum, p, ii) the model presents a mechanical instability transition at small densities, for which scaling laws are analytically predicted and confirmed numerically, iii) the Brillouin peaks persist deep into the unstable phase, the phase transition being noticeable mostly in their linewidth, iv) the Brillouin linewidth scales like p square in the stable phase, and like p in the unstable one. The analytical results are checked numerically for a simple potential. The main features of glassy vibrations previously deduced from scalar ERMT are not substantially altered by these new results.