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The use of the lattice-space Weyl-Wigner formalism of the quantum dynamics of particles in solids, coupled with nonequilibrium Green's-function techniques, provides a rigorous and straightforward derivation of an exact integral form of the equation for a quantum distribution function in many-body quantum-transport theory. We show that with the present formalism more realistic calculations, both numerical (particularly, highly transient simulations) and analytical (fully gauge-invariant calculations), which include full quantum effects and many-body effects, can be carried out in a straightforward, elegant, and physically meaningful manner. This is demonstrated by new results based on a more-accurate numerical simulation procedure and novel applications in terms of ``quantum particle trajectories'' for resonant tunneling diodes, and by a straightforward and fully gauge-invariant formulation of the exact quantum-transport equation of a uniform electron-phonon scattering system in high electric fields, which, for the first time, do not involve any gradient expansion.
Buot et al. (Thu,) studied this question.