Universal heat conductance of one-dimensional channels

TL;DR

This paper demonstrates that the heat and entropy fluxes in one-dimensional channels are universal and independent of particle statistics across all temperatures, linking heat conductance to quantum gas heat capacity.

Contribution

It provides analytical expressions for fluxes in 1D channels for arbitrary statistics and proves their universal temperature dependence.

Findings

Heat and entropy fluxes are independent of particle statistics at all temperatures.

The heat conductance quantum is a low-temperature limit of the 1D channel's heat conductance.

Universal temperature dependence of fluxes is microscopically proven.

Abstract

I analyse the transport of particles of arbitrary statistics (Bose, Fermi and fractional exclusion statistics) through one-dimensional (1D) channels. Observing that the particle, energy, entropy and heat fluxes through the 1D channel are similar to the particle, internal energy, entropy and heat capacity of a quantum gas in a two-dimensional (2D) flat box, respectively, I write analytical expressions for the fluxes at arbitrary temperatures. Using these expressions, I show that the heat and entropy fluxes are independent of statistics at any temperature, and not only in the low temperature limit, as it was previously known. From this perspective, the quanta of heat conductivity represents only the low temperature limit of the 1D channel heat conductance and is equal (up to a multiplicative constant equal to the Plank constant times the density of states at the Fermi energy) to the universal limit of the heat capacity of quantum gases. In the end I also give a microscopic proof for the universal temperature dependence of the entropy and heat fluxes through 1D channels.