Nonanomalous heat transport in a one-dimensional composite chain

TL;DR

This paper investigates how certain one-dimensional composite chains can exhibit normal, Fourier-like heat transport despite translation invariance, proposing a new mechanism involving scale divergence for the transition to anomalous transport.

Contribution

It introduces an alternative mechanism explaining the transition to anomalous heat transport based on scale divergence, supported by analytical analysis of a composite chain model.

Findings

Linear temperature profiles for vanishing elasticity

Fourier's law holds in the continuum limit for finite elasticity

Transition to anomalous transport may occur at diverging scales

Abstract

Translation-invariant low-dimensional systems are known to exhibit anomalous heat transport. However, there are systems, such as the coupled-rotor chain, where translation invariance is satisfied, yet transport remains diffusive. It has been argued that the restoration of normal diffusion occurs due to the impossibility of defining a global stretch variable with a meaningful dynamics. In this Letter, an alternative mechanism is proposed, namely, that the transition to anomalous heat transport can occur at a scale that, under certain circumstances, may diverge to infinity. To illustrate the mechanism, I consider the case of a composite chain that conserves local energy and momentum as well as global stretch, and at the same time obeys, in the continuum limit, Fourier's law of heat transport. It is shown analytically that for vanishing elasticity the stationary temperature profile of the chain is linear; for finite elasticity, the same property holds in the continuum limit.