Phonons in Random Elastic Media and the Boson Peak

TL;DR

This paper investigates how the vibrational density of states in disordered elastic media exhibits a peak, known as the Boson peak, which varies in width depending on the disorder characteristics, impacting understanding of vibrational spectra.

Contribution

It provides a theoretical analysis of the density of states in random elastic media, linking the Boson peak to wave vector ranges between disorder correlation length and interatomic spacing.

Findings

Density of states normalized by frequency squared shows a peak.

Peak width varies from narrow to broad depending on disorder.

Results are relevant for vibrational spectra and light propagation in disordered solids.

Abstract

We show that the density of states of random wave equations, normalized by the square of the frequency, has a peak - sometimes narrow and sometimes broad - in the range of wave vectors between the disorder correlation length and the interatomic spacing. The results of this letter may be relevant for understanding vibrational spectra and light propagation in disordered solids.