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

TL;DR

This paper investigates how one-dimensional diatomic lattices, including FPUT-$eta$ and Toda models, relax to equilibrium when high-frequency optical modes are initially excited, revealing model-dependent thermalization times and universal scaling laws.

Contribution

It introduces the anti-FPUT problem in diatomic lattices, analyzing thermalization dynamics and identifying universal scaling laws in near-integrable regimes.

Findings

Thermalization time depends on whether acoustic or optical modes are thermalized.

Metastable states differ in energy distribution and lifetime between models.

Thermalization time scales inversely with the square of perturbation strength.

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 $T_{\rm eq}$ 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.