Equipartition Threshold in Nonlinear Large Hamiltonian Systems: The Fermi-Pasta-Ulam Model

摘要

The persistence of ordered motions in the thermodynamic limit (N tends to infinity) is analyzed by studying critical energy (Ec) as a function of N and of the initial condition. Numerical experiments support the existence of an equipartition threshold for a nonlinear Hamiltonian system with a large number of degrees of freedom and its persistence as this number is increased. This threshold occurs at the same value of the control parameter, i.e., the energy density, when the number of degrees of freedom varies. The large integration times of the equation of motion suggest a frozen situation. For the N dependence results are unquestionable and in contrast with theoretical predictions, but for time dependence, it is not clear if the threshold vanishes as t approaches infinity. Moreover, an N dependence could be present at much larger times.