Eur. Phys. J. B 66, 165-169 (2008)
https://doi.org/10.1140/epjb/e2008-00393-4

Extended modes and energy dynamics in two-dimensional lattices with correlated disorder

¹ Instituto de Física, Universidade Federal de Alagoas, Maceió AL, 57072-970, Brazil
² GISC, Departamento de Física de Materiales, Universidad Complutense, E-28040 Madrid, Spain

Corresponding author: ^a fidelis@if.ufal.br

Received: 27 August 2008
Revised: 29 September 2008
Published online: 24 October 2008

Abstract

We study the nature of the vibrational modes in a two-dimensional harmonic lattice with long-range correlated random masses, with power-law spectral density S(k)∼1/k^α. We obtain numerically the scale invariance of the fluctuations of the relative participation number and the local density of states. We find signatures of extended vibrational modes when α>α_c and α_c depends on the magnitude of disorder. In order to confirm this claim, we also study the time evolution of an initially localized perturbation of the lattice. We show that the second moment of the spatial distribution of the energy displays a ballistic regime when α>α_c, in agreement with the occurrence of extended vibrational modes.