Delocalization in harmonic chains with long-range correlated random masses

Abstract

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

6 pages, 9 figures

References in corpus (2)

• Onset of Delocalization in Quasi-1D Waveguides with Correlated Surface Disorder
• Reply to comment on "Simple one-dimensional model of heat conduction which obeys Fourier's law"

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