Stochastic transition in two-dimensional Lennard-Jones systems

摘要: We study by computer simulation the behavior at low energy of two-dimensional Lennard-Jones systems, with square or triangular cells and a number degrees freedom $N$ up to 128. These systems exhibit transition from ordered stochastic motions, passing through region intermediate behavior. thus find two stochasticity borders, which separate in phase space ordered, intermediate, regions. The corresponding thresholds have been determined as functions frequency $\ensuremath{\omega}$ initially excited normal modes; they generally increase appear be independent $N$. Their values agree those found other authors for one-dimensional LJ systems. computed also maximal Lyapunov characteristic exponent ${\ensuremath{\chi}}^{*}$ our is typical measure stochasticity; this analysis shows that even certain features may persist. At higher energies, increases linearly per degree $e$. law ${\ensuremath{\chi}}^{*}(e)$ has thermodynamic limit extrapolation. fall physically significant range. function compatible hypothesis on existence classical zero-point energy, advanced Cercignani, Galgani, Scotti.