Ordered and stochastic behavior in a two-dimensional Lennard-Jones system

We study by computer simulation the behavior at low energy of a two-dimensional Lennard-Jones system. The dynamics of the system are analyzed by computing the mean value of the energies of the normal modes, their autocorrelation and cross-correlation functions, and their Fourier spectra. When the energy is lowered the system undergoes a stochastic transition, made evident by qualitative changes occurring in the dynamics. The autocorrelation functions exhibit a twofold behavior: a rapid exponential-like decay which dominates at high energy and a slow decay which dominates at low energy. The Fourier spectrum appears to be continuous at high energy and becomes discrete at low energy. At the lowest energy considered by us, normal modes no longer exhibit a trend toward energy equipartition, at least within the times of our simulation; this fact is due to the onset of selection rules for the energy exchanges among modes. These phenomena occur in a physically significant energy range. For the sake of comparison we have performed a similar analysis on the Hénon-Heiles model, obtaining a relevant concordance.