Fourier's Law for Quasi One--Dimensional Chaotic Quantum Systems

TL;DR

This paper derives Fourier's law for a coherent quasi one-dimensional chaotic quantum system, showing how heat conductance relates to system length and temperature, and providing a quantum mechanical foundation for thermal transport.

Contribution

It provides a derivation of Fourier's law in a quantum chaotic system, linking heat conductance to thermodynamic equilibrium properties and system length.

Findings

Heat conductance is inversely proportional to system length at high temperatures.

Heat conductance can be expressed as an equilibrium coefficient at an intermediate temperature.

The derivation applies to fully coherent, chaotic quantum systems coupled to heat baths.

Abstract

We derive Fourier's law for a completely coherent quasi one--dimensional chaotic quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the level density and, thus, inversely proportional to the length of the system.