Generalized gradient expansions in quantum transport equations

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.