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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 (T0) {0ex{0ex}=0ex{0ex}3L}₀/ (2g+g^2) ---with L₀ the Fermi liquid value---and the conductance 1/2<g<1. For g<1/2 the Lorentz number diverges as T0. Possible relevance to thermal transport in conducting polymer systems is discussed.
Kane et al. (Mon,) studied this question.