Abstract
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 results.
Highlights
Published under licence by IOP Publishing Ltd devices. This result is in striking contrast with the case of mean-field approximations applied to conventional Markov approaches, where the corresponding single-particle equations may lead to positivity violations
Starting from the alternative Markov procedure proposed in Ref. [7], which allows one to derive a global Lindblad scattering superoperator, it is possible to show that such a reduced many-electron dynamics is still of Lindblad type, i.e., dρ =
One has already performed a statistical average over the phonon bath, but the electronic subsystem is still treated via a many-body picture
Summary
This result is in striking contrast with the case of mean-field approximations applied to conventional (non-Lindblad) Markov approaches, where the corresponding single-particle equations may lead to positivity violations. In the investigation of semiconductor-based quantum materials and devices, many of the physical observables of interest (like, e.g., total carrier density, mean kinetic energy, charge current, and so on) may be well described via single-particle electronic operators.
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