Strong stochasticity threshold in some anharmonic lattices

Abstract

Numerical studies have been done on some one-dimensional anharmonic lattices with nearest neighbor interaction. The spectral entropy η and the largest Lyapunov exponent λ 1 were calculated. The diatomic Toda lattice, the Lennard-Jones lattice, and the lattice interacting with 1 r repulsive potential were employed. The present paper aims at investigating how the dynamics of the models is affected by the energy density, paying particular attention to whether the strong stochasticity threshold (SST), as was observed in other models, exits with sufficient generality or not. The results show that the qualitative dependence of the dynamics on the energy density is quite same between the above models. The dynamics is distinguished by two different qualitative behaviors. The dynamics is weakly chaotic in low energy density regime, while it is strongly chaotic in high energy density regime. Evidence for the existence of a rather sharp transition between the two different chaoticity behaviors at a certain critical energy density is provided. Hence, the SST can be defined for all the models employed.