The Boson peak and the phonons in glasses

TL;DR

This paper investigates the origin of the Boson peak in glasses, linking it to a phase transition in the energy landscape from minima to saddle points, supported by theoretical and numerical evidence.

Contribution

It introduces a phase transition framework explaining the Boson peak as a transition in the vibrational energy landscape of amorphous systems.

Findings

Boson peak corresponds to a phase transition in stationary points of energy

Phonons exist in glasses at high frequencies despite disorder

Numerical simulations support the theoretical model

Abstract

Despite the presence of topological disorder, phonons seem to exist also in glasses at very high frequencies (THz) and they remarkably persist into the supercooled liquid. A universal feature of such a systems is the Boson peak, an excess of states over the standard Debye contribution at the vibrational density of states. Exploiting the euclidean random matrix theory of vibrations in amorphous systems we show that this peak is the signature of a phase transition in the space of the stationary points of the energy, from a minima-dominated phase (with phonons) at low energy to a saddle-point dominated phase (without phonons). The theoretical predictions are checked by means of numeric simulations.