Fractional exclusion statistics and the universal quantum of thermal conductance: A unifying approach

Abstract

We introduce a generalized approach to one-dimensional (1D) conduction based on Haldane’s [Phys. Rev. Lett. 67, 937 (1991)] concept of fractional exclusion statistics (FES) and the Landauer formulation [IBM J. Res. Dev. 1, 223 (1957); Phys. Lett. 85A, 91 (1981)] 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 ${\kappa }^{\mathrm{univ}}=({\pi }^2{/3\left)\right(k}_B^{2}T/h)$ 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.