Evaluation of Kubo's Formula for the Impurity Resistance of an Interacting Electron Gas

Abstract

The impurity resistance of an interacting electron gas is evaluated at low but finite temperatures. Analytic techniques similar to those developed by the author for use in the zero-temperature problem are applied to the complete Kubo formula. The calculations are exact to all orders in the electron-electron interactions and to lowest order in the concentration of impurities. To lowest order in the temperature the conductivity is given correctly by the independent quasi-particle model. Corrections of order $T^2$ are discussed in detail. It is shown that the only nonvanishing term of this order which explicitly contains the correlation between two quasi-particles is independent of the impurity concentration, and thus may almost always be neglected.