Timing of the Fermi-Pasta-Ulam-Tsingou Metastable State

The issue of the long metastable state in the Fermi-Pasta-Ulam-Tsingou (FPUT) lattice has been a core concern in Statistical Mechanics since its discovery. The ergodic hypothesis mandates that even arbitrarily small perturbations to a harmonic lattice should allow enough mixing for the time averaged modal energies to equal the ensemble average. However, the metastable state for specific initial conditions has been observed to have a lifetime longer than computationally achievable, for low enough energy. We use a comparison to the Toda lattice to define the end of the metastable state for the α-FPUT model, and then employ a numerical investigation to find the lifetime of this state. In this way, the end of the metastable state demonstrates a transition from nearly integrable dynamics over to non-integrable dynamics. Using many varying initial conditions, we find a scaling of the lifetime of the metastable state for different energies and system sizes. A similar technique is then applied to the β-FPUT model to determine the lifetime of the metastable state. Results are compared to the 'Echo' method which measures the strength of chaos through perturbed reverse integration.