title: Absence of localized acoustic waves in a scale-free correlated random system.
abstract: We numerically study the propagation of acoustic waves in a one-dimensional medium with a scale-free long-range correlated elasticity distribution. The random elasticity distribution is assumed to have a power spectrum S(k) ∼ 1/k(α). By using a transfer-matrix method we solve the discrete version of the scalar wave equation and compute the localization length. In addition, we apply a second-order finite-difference method for both the time and spatial variables and study the nature of the waves that propagate in the chain. Our numerical data indicate the presence of extended acoustic waves for a high degree of correlations. In contrast with local correlations, we numerically demonstrate that scale-free correlations promote a stable phase of free acoustic waves in the thermodynamic limit.
authors.affiliation: Instituto de Física, Universidade Federal de Alagoas, Maceió-AL 57072-970, Brazil.
authors.forename: A E B
authors.initials: AE
authors.lastname: Costa
authors.forename: F A B F
authors.initials: FA
authors.lastname: de Moura