Non-integrability and the Fourier heat conduction law

TL;DR

This paper investigates how nonintegrable dynamics in 1D diatomic chains influence thermal transport, revealing that near-integrable conditions can lead to size-independent heat conductivity, linking microscopic dynamics to macroscopic heat conduction laws.

Contribution

It demonstrates a novel connection between nonintegrability in 1D systems and the persistence of Fourier heat conduction, especially near integrable limits.

Findings

Heat conductivity remains stable over a range of system sizes when the mass ratio is close to one.

As the mass ratio approaches one, the size range for stable heat conductivity expands rapidly.

The results connect microscopic nonintegrable dynamics with macroscopic thermal transport properties.

Abstract

We study in momentum-conserving systems, how nonintegrable dynamics may affect thermal transport properties. As illustrating examples, two one-dimensional (1D) diatomic chains, representing 1D fluids and lattices, respectively, are numerically investigated. In both models, the two species of atoms are assigned two different masses and are arranged alternatively. The systems are nonintegrable unless the mass ratio is one. We find that when the mass ratio is slightly different from one, the heat conductivity may keep significantly unchanged over a certain range of the system size and as the mass ratio tends to one, this range may expand rapidly. These results establish a new connection between the macroscopic thermal transport properties and the underlying dynamics.