Equipartition times in a Fermi-Pasta-Ulam system

We investigate with numerical methods the celebrated Fermi--Pasta--Ulam model, a chain of non--linearly coupled oscillators with identical masses. We are interested in the evolution towards equipartition when energy is initially given to one or a few modes. In previous works we considered the initial energy being given on the lower part of the spectrum. Using the spectral entropy as a numerical indicator we obtained a strong indication that the relaxation time to equipartition increases exponentially with an inverse power of the specific energy. Such a scaling appears to remain valid in the thermodynamic limit. In this paper we explore the dynamics obtained with the initial excitation on the high frequency modes, and we obtain also in this case indication of exponentially long times to equipartition.