Delocalization in harmonic chains with long-range correlated random masses

TL;DR

This paper investigates how long-range correlations in random masses affect vibrational mode localization in harmonic chains, revealing extended modes and ballistic energy spread for certain correlation strengths.

Contribution

It demonstrates the existence of extended vibrational modes in harmonic chains with long-range correlated disorder for  > 1, using transfer matrix and diagonalization methods.

Findings

Extended vibrational modes appear for  > 1.

Ballistic energy spread occurs in this regime.

Anomalous diffusion is observed for weakly correlated disorder.

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.