Thermal Transport in a Luttinger Liquid

We study thermal transport in a one-dimensional (1D) interacting electron gas, employing the Luttinger liquid model. Both thermal conductance and thermopower are analyzed for a pure 1D gas and with impurities. The universal ratio of electrical to thermal conductance in a Fermi liquid—the Wiedemann-Franz law—is modified, whereas the thermopower is still linear in temperature. For a single impurity the Lorentz number is given by L(T→0) = 3L₀/(2g+g²)—with L₀ the Fermi liquid value—and the conductance 1/2<g<1. For g<1/2 the Lorentz number diverges as T→0. Possible relevance to thermal transport in conducting polymer systems is discussed.