Miguel Onorato - Università di Torino #
Route to thermalization in the \(\alpha\)-FPU system #
I consider the \(\alpha\)-FPU system with \(N = 16,32\) and \(64\) masses connected by 
a 
nonlinear 
quadratic spring.  The approach is based on resonant wave-wave interaction theory. I 
will show that the route to thermalization consists of three stages. The first one is 
associated with non-resonant three-wave interactions. At this short time scale, the 
dynamics is reversible; this stage coincides with the observation of recurrent 
phenomena in numerical simulations of the \(\alpha\)-FPU. On a larger time scale, 
exact 
four-wave resonant interactions start to take place; however,  all quartets are 
isolated, preventing a full mixing of energy in the spectrum and thermalization. The 
last stage corresponds to six-wave resonant interactions. Those are responsible for 
the energy equipartition recently observed in numerical simulations. A key role in the 
finding is played by the Umklapp  resonant interactions, typical of discrete systems.
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 The results are obtained in collaboration with Y. Lvov, D. Proment and L. Vozella.