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

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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.