Vendredi 09 novembre 2012 à 14h15
Auditoire Stueckelberg, Ecole de Physique

The Fermi-Pasta-Ulam problem: old ideas, new results

Giancarlo Benettin, Università di Padova

In 1954 Fermi, Pasta and Ulam used one of the firts computers ever constructed to simulate the dynamics of a weakly nonlinear chain of oscillators; the purpose was understanding the time of approach to statistical equilibrium, starting far from it. With surprise they found "an entirely different behavior", and nowadays almost 60 years later, in spite of the temendous progress both in the theory of nonlinear systems and in the power of computers, still the FPU paradox is not completely understood. The aim of the talk is to revisit, in the light of some recent results (still in progress), some old ideas, which seem to us to be the key to understand the subject. Namely: (i) the presence in the problem of two well separated time scales, where different phenomena occurs; (ii) the fact that, in the shorter time scale, the FPU system is essentially integrable, its dynamic being very close not to the corresponding linear model, but to the nonlinear Toda model.