The Femi-Pasta-Ulam-Tsingou system: new developments in the framework of the Wave Turbulence Theory


In the early fifties E. Fermi in collaboration with J. Pasta, S. Ulam and M. Tsingou studied numerically a one-dimensional chain of equal masses connected by a weakly nonlinear spring. One of their goals was to establish the time scale needed for the system to reach a thermalized state. However, instead of thermalization, they observed numerically a recurrence to the initial condition (FPU-recurrence). In the present talk, I will consider the so called β-Fermi-Pasta-Ulam system and, using the approach of the Wave Turbulence Theory based on wave-wave resonant interactions, I will show that the thermal equilibrium is reached regardless of how small is the nonlinearity. The prediction on the relaxation time scale in the weakly nonlinear regime is verified with accurate numerical simulations.