Some properties of large amplitude motion in an anharmonic chain with nearest neighbor interactions

We consider the classical and semiclassical dynamics of a one-dimensional atomic lattice with periodic boundary conditions. Using quasicontinuum approximations, we derive the form of the perfectly periodic vibrational modes of the chain for a cubic and a Lennard-Jones nearest neighbor interaction potential. These long wavelength traveling waves are trains of solitons, rather than harmonic modes, even at low energy. A semiclassical quantization procedure is used to obtain the energy level spectrum for a model anharmonic Xe lattice. The lower eigenenergies are near the harmonic values even though the corresponding classical motion is solitonlike. We show that at high energy the soliton character of the vibrations leads to a breakdown in their stability. This is related to the onset of classical chaos.