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Starting from a recent reformulation of the Markov limit, we apply the mean-field approximation to the resulting Lindblad-type many-electron dynamics, and derive a closed equation of motion for the electronic single-particle density matrix in the presence of one- and two-body scattering mechanisms. The proposed formulation preserves the positive-definite character of the single-particle density matrix. This result is in striking contrast with conventional Markov approaches, where the single-particle mean-field equations can lead to positivity violations and therefore to unphysical result

Microscopic treatment of energy dissipation and decoherence via many-body Lindblad superoperators