Finite thermal conductivity in 1D models having zero Lyapunov exponents

TL;DR

This study investigates heat conduction in 1D channels with zero Lyapunov exponents, revealing that Fourier's law can hold even without chaos, especially in disordered systems.

Contribution

It demonstrates that normal thermal conduction can occur in 1D models with zero Lyapunov exponents, challenging the link between chaos and Fourier's law.

Findings

Fourier heat law observed in disordered channels

Temperature gradient forms in all models

Zero Lyapunov exponents do not prevent normal conduction

Abstract

Heat conduction in three types of 1D channels are studied. The channels consist of two parallel walls, right triangles as scattering obstacles, and noninteracting particles. The triangles are placed along the walls in three different ways: (a) periodic, (b) disordered in height, and (c) disordered in position. The Lyapunov exponents in all three models are zero because of the flatness of triangle sides. It is found numerically that the temperature gradient can be formed in all three channels, but the Fourier heat law is observed only in two disordered ones. The results show that there might be no direct connection between chaos (in the sense of positive Lyapunov exponent) and the normal thermal conduction.