Interrelation between the stability of extended normal modes and the existence of intrinsic localized modes in nonlinear lattices with realistic potentials

Abstract

Previous theoretical studies and molecular dynamics simulations indicate that the anharmonic version of a zone-boundary-mode phonon in a periodic one-dimensional lattice with nearest-neighbor quartic and quadratic interactions is unstable, and that this instability can lead to the production of intrinsic localized modes. We show here that such an instability occurs when nearest-neighbor cubic anharmonicity is added, but that the zone boundary mode is stabilized when the cubic anharmonicity becomes sufficiently large. A direct connection is established between the existence of this instability and the existence of intrinsic localized modes. Furthermore, our analysis reveals the existence of a second type of zone-boundary-mode instability, which is not related to intrinsic localized modes. This ``period-doubling'' instability is also found to occur in one-dimensional lattices with realistic potentials, such as Lennard-Jones, Morse, and Born-Mayer, whereas the instability related to intrinsic localized modes does not occur for these potentials, owing to their inclusion of higher-order anharmonicity. Likewise, intrinsic localized modes are not found in direct numerical searches for these cases, and we conclude that they do not exist in monatomic lattices with these potentials.