Quasiharmonic periodic traveling-wave solutions in anharmonic potentials

Exact solutions of a nonlinear diatomic shell model are investigated in the regime where quasiharmonic and pseudoperiodic traveling waves exist with phonon-type character. The existence regimes of these solutions are determined by the boundary conditions and the model parameters for which especially a strong time and mass dependence is observed. It is found that slowly propagating waves mostly show large displacement responses which can be associated with large dipole moments, while rapidly traveling waves carry a much smaller dipole moment, but still this is appreciably larger than that induced by bare optic-phonon modes. The case of large, anharmonicity shows the opposite effect. Here high-frequency responses carry a large dipole moment. The large dipole moments can be associated with effective charges which induce high oscillator strengths in the corresponding phonon modes, incompatible with results deduced from harmonic lattice dynamics. The origin of the large dipole moments in the shell model is investigated by solving for core and shell displacements separately, where ''acoustic-type'' periodic in-phase displacements of core and shell with different amplitudes are observed, as well as pseudoperiodic out-of-phase ''optic-type'' displacements resulting from large anharmonicity, and are also found in the static limit. Besides the displacement frequency spectrum, the effective potentials are calculated which are distinctly different from phi(4)-type potentials: The potential height is finite with finite width which, in certain cases becomes very small, thus admitting for tunneling through the barrier.