Comment on "Wave-scattering formalism for thermal conductance in thin wires with surface disorder"

TL;DR

This paper clarifies that two seemingly different formulas for thermal conductance in quantum wires are actually consistent, differing only due to the use of different dilogarithm function definitions, emphasizing careful comparison of theoretical results.

Contribution

It resolves apparent discrepancies between two prior theoretical results on quantum wire conductance by identifying the source as different dilogarithm definitions.

Findings

Both formulas are correct when accounting for dilogarithm differences.

Highlights the importance of consistent special function definitions in theoretical physics.

Clarifies previous conflicting results in quantum thermal conductance studies.

Abstract

In their calculations based on the Landauer transport equation, Akguc and Gong [Phys. Rev. B 80, 195408 (2009)] obtained an expression for the heat conductance of a quantum wire valid in the ballistic regime and in the limit of vanishing temperature difference between reservoirs. Their result appears to be different from the one reported in the previous paper of Rego and Kirczenow [Phys. Rev. Lett. 81, 232 (1998)], which led them to argue that their new result was the correct one. We show here that, in fact, both results are correct since different definitions for the dilogarithm function were used in those papers. Hence, comparisons between these two results should be done with care.