The anti-Fermi-Pasta-Ulam-Tsingou problem in one-dimensional diatomic lattices

We study systematically the thermalization dynamics of one-dimensional diatomic lattices (which represents the simplest system possessing multi-branch phonons) of the Fermi-Pasta-Ulam-Tsingou (FPUT)-$\beta$ and the Toda, and focus on how the system relaxes to the equilibrium state when the energy is initially injected into partial the highest-frequency optical modes, which is called the anti-FPUT problem comparing with the original FPUT problem (low frequency excitations of the monatomic lattice). We show numerically that the final thermalization time $T_{\rm eq}$ of the diatomic FPUT-$\beta$ chain depends on whether its acoustic modes are thermalized, whereas the $T_{\rm eq}$ of the diatomic Toda chain depends on the optical ones; in addition, the metastable state of both models have different energy distributions and lifetimes. Despite these differences, in the near-integrable region, the $T_{\rm eq}$ of both models still follows the same scaling law, i.e., $T_{\rm eq}$ is inversely proportional to the square of the perturbation strength. Finally, comparisons of the thermalization behavior between different models under various initial conditions are briefly summarized.