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A definition of ring currents in a velocity vector field is proposed according to topological criteria: ring currents are axial vortices confined in, or rotating beyond, a separatrix, i.e., the boundary which marks the limits of the vortex. Its possible extension to magnetic-field induced, delocalized electron flow in atoms, small non-cyclic molecules and aromatic cyclic compounds is considered.

Graphical abstract: Topological definition of ring currents

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