The Metastable State of the FPUT Problem

We study the approach to thermalization in the Fermi-Pasta-Ulam-Tsingou (FPUT) problem of a chain of non-linearly coupled oscillators. It is expected that these non-linear interactions play a role in the exchange of energy between different modes of the chain leading to equipartition. However, it is observed that giving low to intermediate energies to the initial wave packet results in the formation of a far-from-equilibrium ”metastable” state which can persist for a very long time. We investigate the existence of a critical energy below which the system does not reach equilibrium at all and study this threshold’s dependence on the system’s size. We compare and extend previous studies of the metastable state and find consistency. Further, we compare our results to theoretical predictions made with the multi-wave resonant approach [1].

References

[1] M.D. Bustamante, K. Hutchinson, Y.V. Lvov, and M. Onorato. Exact discrete resonances in the fermi-pasta-ulam–tsingou system. Communications in Nonlinear Science and Numerical Simulation, 73:437–471, 2019.