Breakdown of the Metastable State in the β Fermi-Pasta-Ulam-Tsingou Lattice

We investigate numerically the formation and disappearance of Fermi-Pasta-Ulam-Tsingou (FPUT) recurrences in the β FPUT lattice, with special consideration to the lifespan of the metastable state. First, we consider different initial energies (E) and system sizes (N), to determine which initial parameters cause FPUT recurrences to form. We find that for large N, recurrences cease to form above a critical Eβ, a product of the energy and nonlinear parameter β. We explore the relationship between their disappearance and the breakdown of the metastable state to explain this critical Eβ, and also to estimate the time scale to the metastable state breakdown. In so doing, we define and measure a quantity called “shareable energy” and use this to show that systems with a negative β have a much lower level of energy sharing than those with positive β.