A linear response formalism is developed for evaluation of transport coefficients in quantum many-particle systems. The method is based on a systematic linearization of nonequilibrium Kadanoff-Baym transport equations in an integral form in ac electric fields. Simple and consistent approximations can be performed in the resulting set of transport equations, which replace vertex equations in the Kubo formalism. The method is illustrated by the example of an ac and dc conductivity and conductance for a quasi-one-dimensional electron system with an electron--phonon interaction for three-dimensional acoustical phonons. After approximations standard in metals, the solved transport equations coincide with the Holstein equation. \textcopyright{} 1996 The American Physical Society.
Gradient expansions in quantum transport equations of a Kadanoff–Baym form have been reexamined. We have realized that in a consistent approach the expansion should be performed also inside of the self–energy in the scattering integrals of these equations. In the first perturbation order this internal expansion gives new correction terms to the generalized Boltzman equation. These correction terms are found here for several typical systems. Possible corrections to the theory of a linear response to weak electric fields are also discussed. 1 1