Quantum Boltzmann equation and Kubo formula for electronic transport in solids

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Abstract
We present a derivation of the quantum Boltzmann equation for linear dc transport with a correction term to the Mahan-Hansch equations and derive a formal solution to it. Based on this formal solution, we find the electric conductivity can be expressed as the retarded current-current correlation. Therefore we explicitly demonstrate the equivalence of the two most important theoretical methods: the quantum Boltzmann equation and the Kubo formula.