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

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.