Generalized gradient expansions in quantum transport equations

TL;DR

This paper revisits gradient expansions in quantum transport equations, revealing that internal expansion within the self-energy introduces new correction terms to the generalized Boltzmann equation, impacting linear response theories.

Contribution

It introduces a consistent approach to gradient expansions by including internal expansion within the self-energy, leading to novel correction terms in quantum transport equations.

Findings

Derived correction terms for typical systems

Identified impact on linear response to electric fields

Proposed a more consistent expansion methodology

Abstract

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.