Topological invariants of electronic currents in magnetic fields

TL;DR

This paper presents a topological framework for understanding quantum electronic currents in magnetic fields, linking divergence to magnetic coupling and analyzing electronic wave signals through Fourier analysis from first principles.

Contribution

It introduces a novel topological interpretation of quantum magnetic phenomena and provides an ab initio Fourier analysis of electronic wave signaling.

Findings

Topological invariants characterize quantum electronic currents.

Divergence relates to magnetic coupling via a Cern invariant vector.

Fourier analysis reveals electronic wave behavior from first principles.

Abstract

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}.