Crossover of dynamical instability and chaos in the supercritical state

We calculate the maximal Lyapunov exponent for a bulk system of 256 Lennard-Jones particles in constant energy molecular dynamics simulations deep into the supercritical state. We find that the maximal Lyapunov exponent undergoes a crossover and that this crossover coincides with the dynamical crossover at the Frenkel line from liquid physics. We explain this crossover in terms of two different contributions to dynamical instability: diffusion in the liquidlike state below the Frenkel line and collisions in the gaslike state above. These results provide insight into the phase-space dynamics far from the melting line and densities where rare-gas approximation are inapplicable.