Nonlinear Phonon Modes in Second Order Anharmonic Coupled Monoatomic Chains

Abstract

We have used multipletimescales perturbation theory as well as the numerical methods of molecular dynamics and spectral energy density (SED) to investigate the phonon band structure of a twochain model with secondorder anharmonic interactions. We show that when one chain is linear and the other is nonlinear, the twochain model exhibits a nonlinear resonance near a critical wave number due to mode selfinteraction. The nonlinear resonance enables wave numberdependent interband energy transfer. We have also shown that there exist nonlinear modes within the spectral gap separating the lower and upper branches of the phonon band structure. These modes result from three phonon interactions between a phonon belonging to the nonlinear branch and two phonons lying on the lower branch. This phenomenon offers a mechanism for phonon splitting.