Abstract
The vibrational modes with nonzero frequency are localized in harmonic lattice with disordered masses. In our work, we investigated numerically the propagation of vibrational energy in harmonic lattice with long-range correlated disordered masses, which are randomly distributed with power law spectrum S ( k ) ∝ k - α . For α = 0, a standard uncorrelated disordered mass distribution was observed and for α > 0 its distribution exhibits intrinsic long-range correlations. Our procedure was done by the numerical solution of the classical equations for the mass displacement and velocities. Energy flow was investigated after injection of an initial wave-packet with energy E0 and the dynamics of the vibrational energy wave-packet was analyzed. We also investigated the dynamics of a pulse pumped at one side of the lattice. Our calculations suggest that vibrational modes with nonzero frequency propagate within harmonic lattice with correlated disordered masses distribution.
Highlights
The propagation of general particles in disordered systems represents an interesting issue with several connections with solid state physics, acoustics, electrodynamics, biological systems and other branches of science
Authors gave numerical proof of the smoothness of local disorder as the correlation parameter α increases. It is a consequence of the Fourier method used to generate the correlated disorder
In disordered harmonic chains, it was demonstrated that the Anderson Localization Theory works for high frequencies, but modes around ω = 0 can propagate even for strong disorder (Dean 1964, Datta and Kundu 1994)
Summary
The propagation of general particles in disordered systems represents an interesting issue with several connections with solid state physics, acoustics, electrodynamics, biological systems and other branches of science. Vibrational modes with high frequencies in one-dimensional (1D) harmonic chains with a random sequence of masses are localized (D√ean 1964). Our calculations suggest that intrinsic correlations, which exists within the masses’ distribution, promotes a ballistic energy flux throughout those disordered systems.
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