Prethermalization in Fermi-Pasta-Ulam-Tsingou chains

Abstract: The observation of the Fermi-Pasta-Ulam-Tsingou (FPUT) paradox, namely the lack of equipartition in the evolution of a normal mode in a nonlinear chain on unexpectedly long times, is arguably the most famous numerical experiment in the history of physics. Since seventy years after its publication, most studies in FPUT chains still focus on long wavelength initial states similar to the original paper. It is shown here that all characteristic features of the FPUT paradox are rendered even more striking if short(er) wavelength modes are evolved instead. Since not every normal mode leads to equipartition, we also provide a simple technique to predict which modes, and in what order, are excited starting from an initial mode (root) in $\alpha$-FPUT chains. The excitation sequences associated with a root are then shown to spread energy at different speeds, leading to prethermalization regimes that become longer as a function of mode excitation number. This effect is visible in observables such as mode energies and spectral entropies and, surprisingly, also in the time evolution of invariant quantities such as Lyapunov times and Kolmogorov-Sinai entropies. Our findings generalize the original FPUT experiment, provide an original look at the paradox's source, and enrich the vast literature dedicated to studying equipartition in classical many-body systems.