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

We study the thermalization dynamics of one-dimensional diatomic lattices (which represents the simplest system possessing multi-branch phonons), exemplified by the famous Fermi-Pasta-Ulam-Tsingou (FPUT)-beta and the Toda models. Here we focus on how the system relaxes to the equilibrium state when part of highest-frequency optical modes are initially excited, which is called the anti-FPUT problem comparing with the original FPUT problem (low frequency excitations of the monatomic lattice). It is shown numerically that the final thermalization time T (eq) of the diatomic FPUT-beta chain depends on whether its acoustic modes are thermalized, whereas the T (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 (eq) of both models still follows the same scaling law, i.e. T (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.