Generalized Local Charge Conservation in Many-Body Quantum Mechanics

In the framework of the quantum theory of many-particle systems, we study the compatibility of approximated Non-Equilibrium Green Functions (NEGFs) and of approximated solutions of the Dyson equation with a modified continuity equation of the form ∂t〈ρ〉+(1−γ)∇·〈J〉=0. A continuity equation of this kind allows the e.m. coupling of the system in the extended Aharonov-Bohm electrodynamics, but not in Maxwell electrodynamics. Focusing on the case of molecular junctions simulated numerically with the Density Functional Theory (DFT), we further discuss the re-definition of local current density proposed by Wang et al., which also turns out to be compatible with the extended Aharonov-Bohm electrodynamics.