The Metastable State of Fermi-Pasta-Ulam-Tsingou Models.

Classical statistical mechanics has long relied on assumptions such as the equipartition theorem to understand the behavior of the complicated systems of many particles. The successes of this approach are well known, but there are also many well-known issues with classical theories. For some of these, the introduction of quantum mechanics is necessary, e.

The β Fermi-Pasta-Ulam-Tsingou recurrence problem.

We perform a thorough investigation of the first Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence in the β-FPUT chain for both positive and negative β. We show numerically that the rescaled FPUT recurrence time T=t/(N+1) depends, for large N, only on the parameter S≡Eβ(N+1). Our numerics also reveal that for small |S|, T is linear in S with positive slope for both positive and negative β.