  In this article it is reported a formulation of the solenoidal nature of
quantum electronic currents at the nanoscale whose divergence is expressed as
the coupling of a magnetic field, interacting with a quantum body, and a
weighted Cern invariant vector making then a direct topological interpretation
of this quantum magnetic phenomenon. Also a Fourier analysis of the signaling
of electronic waves is reported in an ab initio formalism from first
pinciples\cite{Martin}.
