# Nonintegrability and thermalization of one-dimensional diatomic lattices

## TL;DR

This study investigates how breaking integrability in one-dimensional diatomic lattices affects thermalization, revealing a universal inverse-square law for thermalization time regardless of the method used to break integrability.

## Contribution

It demonstrates that different methods of destroying integrability lead to distinct thermalization pathways but share a universal inverse-square relationship for thermalization time.

## Key findings

- Thermalization time scales inversely with the square of perturbation strength.
- Different methods of breaking integrability produce qualitatively different thermalization routes.
- Universal law of thermalization time applies across different 1D diatomic lattice models.

## Abstract

Nonintegrability is a necessary condition for the thermalization of a generic Hamiltonian system. In practice, the integrability can be broken in various ways. As illustrating examples, we numerically studied the thermalization behaviors of two types of one-dimensional (1D) diatomic chains in the thermodynamic limit. One chain was the diatomic Toda chain whose nonintegrability was introduced by unequal masses. The other chain was the diatomic Fermi-Pasta-Ulam-Tsingou-$\beta$ chain whose nonintegrability was introduced by quartic nonlinear interaction. We found that these two different methods of destroying the integrability led to qualitatively different routes to thermalization, but the thermalization time, $T_{eq}$, followed the same law; $T_{eq}$ was inversely proportional to the square of the perturbation strength. This law also agreed with the existing results of 1D monatomic lattices. All these results imply that there is a universal law of thermalization that is independent of the method of breaking integrability.