Fermi Pasta Ulam system - new ideas about old problem.
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
This is a joint work with Miguel Onorato, Lara Vozella
and Davide Proment.