Thermal Conductivity of a System of Interacting Electrons

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Abstract
Kubo's formula for thermal conductivity is evaluated for the case of an interacting electron gas and random, fixed, impurities. As in previous work, the theorems proved are exact to all orders in the electron-electron interactions and to lowest order in the concentration of impurities. The heat flux is examined in some detail and a Ward's identity is derived for the associated vertex function. Although the heat flux contains contributions from the interaction energy of pairs (or larger clusters) of correlated quasi-particles, it is found that these contributions enter the thermal conductivity only to higher orders in the impurity concentration. In a normal system where the many-body correlations are sufficiently weak, the Wiedemann-Franz law remains valid.