EQUIVALENCE OF QUANTUM BOLTZMANN EQUATION AND KUBO FORMULA FOR dc CONDUCTIVITY

We present a derivation of the quantum Boltzmann equation for linear dc transport with a correction term to Mahan-Hansch's 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: quantum Boltzmann equation and Kubo formula.