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 $\partial_t \langle \rho \rangle+(1-\gamma)\nabla\cdot \langle\mathbf{J} \rangle=0$. 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.