Nonintegrability and thermalization of one-dimensional diatomic lattices

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.

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Cited by in corpus (10)

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• Effect of pressure on thermalization of one-dimensional nonlinear chains
• The anti-Fermi-Pasta-Ulam-Tsingou problem in one-dimensional diatomic lattices
• Thermalization of isolated harmonic networks under conservative noise
• Large-deviations approach to thermalization: the case of harmonic chains with conservative noise
• Thermalization in asymmetric harmonic chains
• Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems
• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport