Anderson universality in a model of disordered phonons

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Pinski, Sebastian D. ; Schirmacher, Walter ; Roemer, Rudolf A. (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.
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    1Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom∗ 2Institut fu¨r Physik, Universita¨t Mainz, D-55099 Mainz, Germany and Physik-Department E13, Technische Universita¨t Mu¨nchen, D-85747 Garching, Germany (Dated: Revision : 1.42, compiled Wednesday 24th August, 2011, 01:51) ∗ Corresponding author: s.d.pinski@warwick.ac.uk

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