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 LsT ! 0d ­ 3L0ys2g 1 g2d—with L0 the Fermi liquid value—and the conductance 1y2 , g , 1. For g , 1y2 the Lorentz number diverges as T ! 0. Possible relevance to thermal transport in conducting polymer systems is discussed.