Anderson universality in a model of disordered phonons

TL;DR

This paper investigates how disorder affects wave localization in a lattice of coupled masses and springs, revealing Anderson-type phase transitions and their universality in disordered phononic systems.

Contribution

It provides the first comprehensive phase diagrams for disordered phonon models and demonstrates the universality of localization transitions through high-precision numerical analysis.

Findings

Existence of delocalization-localization transitions in disordered phonon systems

Phase diagrams showing stable and unstable wave modes

Confirmation of Anderson universality in phonon localization transitions

Abstract

We consider the localization properties of a lattice of coupled masses and springs with random mass and spring constant values. We establish the full phase diagrams of the system for pure mass and pure spring disorder. The phase diagrams exhibit regions of stable as well as unstable wave modes. The latter are of interest for the instantaneous-normal-mode spectra of liquids and the nascent field of acoustic metamaterials. We show the existence of delocalization-localization transitions throughout the phase diagram and establish, by high-precision numerical studies, that the universality of these transitions is of the Anderson type.