Anderson universality in a model of disordered phonons

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.

5 pages, 2 figures, 1 table

References in corpus (28)

• Anderson Transitions
• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Localization of ultrasound in a three-dimensional elastic network
• Observation of the critical regime near Anderson localization of light
• Experimental observation of the Anderson transition with atomic matter waves
• Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"
• Corrections to scaling at the Anderson transition
• Visualizing Critical Correlations near the Metal-Insulator Transition in Ga1-xMnxAs
• Continuum limit of amorphous elastic bodies (III): Three dimensional systems
• The Quantum Hall Transition in Real Space: From Localized to Extended States
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Between a metal and an insulator: the critical state of the Anderson transition
• Observation of multifractality in Anderson localization of ultrasound
• Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves: Theory and Experiment
• Direct comparison between potential landscape and local density of states in a disordered two-dimensional electron system
• The two-dimensional Anderson model of localization with random hopping
• Excess Modes in the Vibrational Spectrum of Disordered Systems and the Boson Peak
• Critical Exponents for the Metal--Insulator Transition in Disordered Systems
• Anderson localization of phonons in dimension $d=1,2,3$ : finite-size properties of the Inverse Participation Ratios of eigenstates
• Extended Fractons and Localized Phonons on Percolation Clusters
• Disorder-Induced Vibrational Localization
• Anderson Localization in Euclidean Random Matrices
• Power-law Localization in 2D, 3D with Off-diagonal Disorder
• Localization threshold of Instantaneous Normal Modes from level-spacing statistics
• Localization-delocalization transition for disordered cubic harmonic lattices
• Scaling of the localization length in linear electronic and vibrational systems with long-range correlated disorder
• Anderson transition of three dimensional phonon modes

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