Abstract
We numerically study the propagation of acoustic waves in a one-dimensionalmedium with a scale-free long-range correlated elasticity distribution.The random elasticity distribution is assumed to have a power spectrumS(k) ∼ 1/kα. By using a transfer-matrix method we solve the discrete version of the scalar waveequation and compute the localization length. In addition, we apply a second-orderfinite-difference method for both the time and spatial variables and study the nature of thewaves that propagate in the chain. Our numerical data indicate the presence of extendedacoustic waves for a high degree of correlations. In contrast with local correlations, wenumerically demonstrate that scale-free correlations promote a stable phase of free acousticwaves in the thermodynamic limit.
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