# Open Quantum Systems: Limitations of Self-Energy Method

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In low field quantum transport, steady state regime, a popular method to compute Non-Equilibrium Green's functions to study transport, as introduced by Datta (see for reference pdf), accounts for open boundary conditions through a self-energy of interaction term.

However, this method (to account for open boundary conditions) has been criticized by Knezevic in his paper (pdf). I also quote the exact statement here as follows,

"In low field, steady state regime, the variant of Non-Equilibrium Green’s function formalism introduced by Datta and co-workers accounts for open boundary conditions through a special injection self-energy term, where the electrons are injected from each contact with the contact’s equilibrium distribution. However, there is no kinetic theory showing that this is indeed the steady state that the system relaxes to upon the application of bias, nor how the results would look in the high field regime or during the transients. It is now well accepted that the treatment of contacts is crucial for describing the relaxation in the absence of frequent scattering. However, a general description of the contact-induced decoherence (nonunitary dynamics) in nanoscale devices is lacking."

While this statement suggests that since there is no kinetic theory that supports the steady state predicted by the method, hence its applicability comes to question. However, is there any limitation of the self-energy method that should be a concern. Is there any scenario in which the self-energy method (in low field transport) fails? Is there any assumption made in the derivation of the self-energy method (as boundary conditions to open quantum systems) that can be challenged physically?

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