Delocalization in harmonic chains with long-range correlated random masses

Details Delocalization in harmonic chains with long-range correlated random masses Delocalization in harmonic chains with long-range correlated random masses

2002-09-13

arxiv.org/abs/cond-mat/0209304v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 9 figures

Scientific paper

10.1103/PhysRevB.68.012202

We study the nature of collective excitations in harmonic chains with masses exhibiting long-range correlated disorder with power spectrum proportional to $1/k^{\alpha}$, 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 $\alpha > 1$. 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 $\alpha>1$ due to the presence of extended vibrational modes.

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