Stationary anharmonic gap modes in diatomic aperiodic lattices

We investigate numerically, within the rotating wave approximation, the existence of stationary anharmonic localized modes in diatomic lattices, where the atoms are ordered according to the Thue-Morse sequence and the Fibonacci sequence, respectively. A symmetric potential with harmonic and quartic terms is used, and both the case of hard and soft anharmonicity is investigated. We find the existence of localized modes for frequencies not allowed in the harmonic approximation, both when we consider hard and soft anharmonicity in the potential. Above the top of the allowed frequency values, there turn out to be only modes with a hard anharmonicity. In contrast to the periodic chains previously investigated, we find for the Thue-Morse lattice even modes which seem to be stable in molecular-dynamics simulations.