Yuri Lvov, Rensselaer Polytechnic Institute

Abstract: Despite the fact that more than 60 years have passed, the Fermi–Pasta–Ulam (FPU) system has not yet been fully understood.We study the alpha -FPU problem by applying the wave–wave interaction theory. We find that the first non trivial resonances correspond to six-wave interactions. Those are precisely the interactions responsible for the thermalization of the energy in the spectrum. We predict that for small amplitude random waves the time scale of such interactions is extremely large and it is of the order of $1/\epsilon^8$, where $\epsilon$ is the small parameter in the system. This is why the emergence of equipartition requires very long times. The wave-wave interaction theory is not based on any threshold: equipartition is predicted for arbitrary small nonlinearity.

This is a joint work with Miguel Onorato, Lara Vozella and Davide Proment.