Transport equations for many-particle systems

The formalism of Kadanoff and Baym is used to derive a new transport equation for many-particle systems in dc electric fields. We use it to derive the conductivity of a metal, when limited by the electron-phonon interaction. The final result is identical to Holstein's formula, which he derived from the Kubo formula. We also solved two other problems: the electrical current in a system limited by Gaussian white noise, and the diffusion coefficient from impurity scattering. We also discuss the lack of thermal stability in particle systems limited by Gaussian white noise.