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

Abstract

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 $T_{\mathrm{eq}}$ of the diatomic FPUT-$\beta$ chain depends on whether its acoustic modes are thermalized, whereas the $T_{\mathrm{eq}}$ 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 $T_{\mathrm{eq}}$ of both models still follows the same scaling law, i.e., $T_{\mathrm{eq}}$ 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.

arXiv comment13 pages, 6 figures

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Cited by in corpus (2)

• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport
• Thermalization in asymmetric harmonic chains