# Low-frequency excitations and their localization properties in glasses

## TL;DR

This paper investigates the localization properties of low-frequency vibrational modes in glasses, revealing a crossover behavior near the dynamical transition temperature and under random pinning, shedding light on anomalous thermodynamic features.

## Contribution

It provides new insights into the localization and distribution of low-frequency modes in glasses, especially near the dynamical transition and with random pinning.

## Key findings

- Crossover in the inverse participation ratio distribution near the dynamical transition temperature.
- Similar crossover observed at high parental temperature with random pinning.
- Low-frequency modes are linked to anomalous thermodynamic features in glasses.

## Abstract

Besides the dynamical slowing down signaled by an enormous increase of the viscosity approaching the glass transition, structural glasses show interesting anomalous thermodynamic features at low temperatures that hint at peculiar deviations from Debye's law at low enough frequencies. Theory, numerical simulations, and experiments suggest that deviation from Debye's law is due to soft-localized glassy modes that populate the low-frequency spectrum. We study the localization properties of the low-frequency modes in a three-dimensional supercooled liquid model. The density of states $D(\omega)$ is computed considering the inherent structures of configurations well thermalized at parental temperatures close to the dynamical transition $T_\text d$. We observe a crossover in the probability distribution of the inverse of the participation ratio that happens approaching $T_\text d$ from high temperatures. We show that a similar crossover is observed at high parental temperature when the translational invariance of the system is explicitly broken by a random pinning field.