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

Miguel Onorato
Università’ di Torino
Wednesday, March 8, 2017 - 14:00

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 (this is known as the FPUT-recurrence). This unexpected result has lead to the development of the modern nonlinear physics (discovery of solitons, integrability etc). In the present talk, I will consider the so called β-Fermi-Pasta-Ula 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.

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