Vanishing stability thresholds in the thermodynamic limit of nonintegrable conservative systems

Abstract

We study numerically the transition to stochasticity in the Fermi-Pasta-Ulam model and its dependence on the number of degrees of freedom of the system. Via a normalized spectral entropy we define a critical value of the energy density where the transition takes place. While in the special case of single-mode excitation the critical energy density remains constant in the thermodynamic limit, it is roughly inversely proportional to the system size, if we start with a superposition of many excited normal modes. In the first case we are able to confirm the numerical results with analytical considerations, whereas the results of the latter case are compared with analytic estimates obtained by Chirikov.