2011/07/31 by Sebastian D. Pinski, Walter Schirmacher, Rudolf A. Römer +1 · 1 citation
Engineering · Materials Science · Physics and Astronomy · #Acoustic Wave Phenomena Research #Acoustic metamaterials #Anderson localization #Condensed matter physics #Lattice (music) #Material Dynamics and Properties #Metamaterial #Nonlinear Photonic Systems #Phase (matter) #Phase diagram #Phase transition #Phonon #Physics #Quantum mechanics #Statistical physics #Universality (dynamical systems) #cond-mat.dis-nn
paper · pdf · doi:10.1209/0295-5075/97/16007
published as EPL 97, 16007-6 (2012) · 5 pages, 2 figures, 1 table
arxiv created 2011/08/23 · openalex publication_date 2012/01/01 · arxiv updated 2012/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the localisation 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 delocalisation-localisation transitions throughout the phase diagram and establish, by high-precision numerical studies, that the universality of these transitions is of the Anderson type.