Quantum structure of glasses and the boson peak: a theory of vibrations

TL;DR

This paper introduces a new analytical model for glasses that explains the boson peak as a consequence of noncommutative geometry in fluid-like disorder, successfully matching experimental data across various amorphous materials.

Contribution

It proposes a novel first-principles model linking fluid disorder to vibrational properties in glasses, explaining the boson peak through noncommutative geometry effects.

Findings

Model accurately predicts specific heat in amorphous silicon, vitreous GeO₂, and Ba₈Ga₁₆Sn₃₀.

The boson peak arises from van Hove singularity induced by noncommutative geometry.

Universal applicability demonstrated across different glassy materials.

Abstract

We present a novel analytical model for glasses, starting from the first principle that the disorder in a glass mimics the disorder in a fluid. The origin of the boson peak is attributed to the intrinsically noncommutative geometry of the fluid disorder, which induces a van Hove singularity in the vibrational density of states. The universality of the model is exhibited by applying it to amorphous silicon, vitreous GeO$_2$ and Ba$_{8}$Ga$_{16}$Sn$_{30}$ clathrate, which show a remarkable agreement between the theoretical predictions for specific heat and the experimental data.