Seminar announcement

[Emanuele Tuillier Illingworth]

*Mathematical Physics Seminar*

*Wednesday the 8th of March  2.00-3.00pm Room 005  SISSA main building*
*Speaker: Miguel Onorato*
*Title: The Femi-Pasta-Ulam-Tsingou problem: new developments in the *
*framework of the Wave Turbulence Theory*

Abstract: 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.