A random matrix approach to the boson peak and Ioffe-Regel criterion in amorphous solids

TL;DR

This paper uses random matrix theory to analytically and numerically investigate vibrational properties of amorphous solids, revealing the boson peak, Ioffe-Regel crossover, and quasilocalized vibrations.

Contribution

It introduces a random matrix framework to analytically describe vibrational density of states and dynamical structure factors in amorphous solids, connecting these to the boson peak and Ioffe-Regel criterion.

Findings

Analytical form of vibrational density of states derived

Identification of Ioffe-Regel crossover point

Numerical model shows quasilocalized vibrations with power-law density of states

Abstract

We present a random matrix approach to study general vibrational properties of stable amorphous solids with translational invariance using the correlated Wishart ensemble. Within this approach, both analytical and numerical methods can be applied. Using the random matrix theory, we found the analytical form of the vibrational density of states and the dynamical structure factor. We demonstrate the presence of the Ioffe-Regel crossover between low-frequency propagating phonons and diffusons at higher frequencies. The reduced vibrational density of states shows the boson peak, which frequency is close to the Ioffe-Regel crossover. We also present a simple numerical random matrix model with finite interaction radius, which properties rapidly converges to the analytical results with increasing the interaction radius. For fine interaction radius, the numerical model demonstrates the presence of the quasilocalized vibrations with a power-law low-frequency density of states.