Properties of one-dimensional nonlinear vibrational modes in triangular lattice with Lennard-Jones interactions

Abstract

Crystal lattices support delocalized nonlinear vibrational modes (DNVMs), which are determined solely by the lattice point symmetry, and are exact solutions of the equations of atomic motion for any interatomic potential. DNVMs can be used for setting initial conditions to excite spatially localized vibrational modes called discrete breathers (DBs). In this study, DNVMs derived for instability can result in the formation of localized vibrational modes concentrating a significant part of the lattice energy. In some cases, localized vibrational modes can be obtained by imposing localizing functions upon DNVM.

Discrete breathers in a triangular β -Fermi-Pasta-Ulam-Tsingou lattice

“…where A denotes the DNVM amplitude. Later, in [110], these modes were excited in a close-packed atomic row of a triangular Lennard-Jones lattice. The obtained vibrational modes were called one-dimensional DBs.…”