The Fermi-Pasta-Ulam problem and the metastability perspective

A review is given of the works on the FPU problem that were particularly relevant in connection with the metastability perspective, proposed in the year 1982. The idea is that there exists a specific energy threshold above which the time-averages of the relevant quantities quickly agree with the predictions of classical equilibrium statistical mechanics, whereas below it there exist two time scales. First there is a quick formation of a packet of low-frequency modes which do share the energy, and this produces a metastable state that lasts for a long time; then the system attains the final equilibrium state. There are strong indications that the specific energy threshold does not vanish in the limit of infinitely many particles. The review is given for the case of a one-dimensional FPU chain.