Are Current Discontinuities in Molecular Devices Experimentally Observable?

An ongoing debate in the first-principles description of conduction molecular devices concerns correct definition current presence non-local potentials. If physical density ${\bf j}=(-ie\hbar/2m)(\Psi^* \nabla \Psi- \Psi \Psi^*)$ is not locally conserved but can be re-adjusted by a term, which should regarded as real? We prove that extended Maxwell equations Aharonov-Bohm give e.m.\ field generated such currents without any ambiguity. For an oscillating dipole we show radiated electrical has longitudinal component proportional to $ \omega \hat{P}$, where $\hat{P}$ anomalous moment $\int \hat{I}(\mathbf{x})\mathbf{x} d^3x$ and $\hat{I}$ space-dependent part anomaly $I=\partial_t \rho+\nabla \cdot \mathbf{j}$. In case stationary device, failure local conservation causes "missing field" effect experimentally observable, especially if its entity depends on total current.