Anderson universality in a model of disordered phonons
Department of Physics and Centre for Scientific Computing, University of Warwick Coventry, CV4 7AL, UK, EU
2 Dipartimento di Fisica, Universitá di Roma “La Sapienza” - I-00185, Roma, Italy, EU
3 Institut für Physik, Universität Mainz - D-55099 Mainz, Germany, EU
Accepted: 23 November 2011
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.
PACS: 63.20.D- – Phonon states and bands, normal modes, and phonon dispersion / 63.20.Pw – Localized modes / 63.50.-x – Vibrational states in disordered systems
© EPLA, 2012