Fractional Exclusion Statistics and the Universal Quantum of Thermal Conductance: A Unifying Approach

TL;DR

This paper presents a unifying theoretical framework for 1D thermal conductance based on fractional statistics, demonstrating its universality and contrasting it with the statistics-dependent electrical conductance.

Contribution

It introduces a generalized approach combining fractional exclusion statistics with Landauer transport theory, revealing the universal quantum of thermal conductance in 1D systems.

Findings

Thermal conductance is universal and independent of carrier statistics.

Electrical conductance depends on the statistics obeyed by carriers.

Unifies theories of electron and phonon transport in 1D systems.

Abstract

We introduce a generalized approach to one-dimensional (1D) conduction based on Haldane's concept of fractional statistics (FES) and the Landauer formulation of transport theory. We show that the 1D ballistic thermal conductance is independent of the statistics obeyed by the carriers and is governed by the universal quantum $ (\pi^2 k^2_B T)/(3h) $ in the degenerate regime. By contrast, the electrical conductance of FES systems is statistics-dependent. This work unifies previous theories of electron and phonon systems and explains an interesting commonality in their behavior.