Propagation of vibrational modes in classical harmonic lattice with correlated disorder

Leonade D DA Silva; Adhemar Ranciaro Neto; Messias O Sales; José L L Dos Santos; Francisco A B F DE Moura

doi:10.1590/0001-3765201920180114

Propagation of vibrational modes in classical harmonic lattice with correlated disorder

An Acad Bras Cienc. 2019 Jul 1;91(2):e20180114. doi: 10.1590/0001-3765201920180114.

Authors

Leonade D DA Silva¹, Adhemar Ranciaro Neto², Messias O Sales³, José L L Dos Santos⁴, Francisco A B F DE Moura¹

Affiliations

¹ Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió, AL, Brazil.
² Faculdade de Economia, Administração e Contabilidade, 57072-970 Maceió, AL, Brazil.
³ Instituto Federal do Maranhão/IFMA, Campus São João dos Patos, Rua Padre Santiago, s/n, Centro, 65665-000 São João dos Patos, MA, Brazil.
⁴ Escola de Educação Básica e Profissional Fundação Bradesco, Avenida Presidente Vargas, s/n, Serraria, 57046-140 Maceió, AL, Brazil.

PMID: 31269101
DOI: 10.1590/0001-3765201920180114

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.