Reconstructing Fourier's law from disorder in quantum wires

TL;DR

This paper demonstrates how increasing disorder in quantum wires induces a transition from non-Fourier to Fourier's law behavior, linking disorder to thermal conduction properties in nanoscale systems.

Contribution

It reveals that disorder in quantum wires causes the emergence of Fourier's law, with the local temperature gradient and heat current relationship being explicitly characterized.

Findings

Ballistic wires show almost uniform temperature and violate Fourier's law.

Disorder induces a uniform temperature gradient and linear heat current relation.

Energy distribution is governed solely by heat baths, independent of disorder.

Abstract

The theory of open quantum systems is used to study the local temperature and heat currents in metallic nanowires connected to leads at different temperatures. We show that for ballistic wires the local temperature is almost uniform along the wire and Fourier's law is invalid. By gradually increasing disorder, a uniform temperature gradient ensues inside the wire and the thermal current linearly relates to this local temperature gradient, in agreement with Fourier's law. Finally, we demonstrate that while disorder is responsible for the onset of Fourier's law, the non-equilibrium energy distribution function is determined solely by the heat baths.