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Delocalization in harmonic chains with long-range correlated random masses

F. A. B. F. de Moura·M. D. Coutinho-Filho·E. P. Raposo·M. L. Lyra
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Abstract

We study the nature of collective excitations in harmonic chains with masses exhibiting long-range correlated disorder with power spectrum proportional to $1/k^α$, where $k$ is the wave-vector of the modulations on the random masses landscape. Using a transfer matrix method and exact diagonalization, we compute the localization length and participation ratio of eigenmodes within the band of allowed energies. We find extended vibrational modes in the low-energy region for $α> 1$. In order to study the time evolution of an initially localized energy input, we calculate the second moment $M_2(t)$ of the energy spatial distribution. We show that $M_2(t)$, besides being dependent of the specific initial excitation and exhibiting an anomalous diffusion for weakly correlated disorder, assumes a ballistic spread in the regime $α>1$ due to the presence of extended vibrational modes.

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F. A. B. F. de Moura, M. D. Coutinho-Filho, E. P. Raposo, M. L. Lyra. 2002-09-13. Delocalization in harmonic chains with long-range correlated random masses. https://doi.org/10.1103/physrevb.68.012202

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