Thermal Conductivity and Lorenz Number for One-Dimensional Ballistic Transport

We study the thermal conductivity and Lorenz number of charge carriers for one-dimensional ballistic transport within the correlation function formalism. The carrier transit time between two ideal contacts is found to substitute for the collision time in the definition of a ballistic thermal conductivity. A universal thermal conductance $K=2\mathrm{}{\pi }^2{k}_B^{2}T/3h$ is naturally obtained for the degenerate case. Dispersion curves for the thermal conductivity and the Lorenz number associated with different time scales belonging to the microscopic system are given for the first time.