It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines with an arbitrary value of magnetic flux can be used to create energetic barriers, which can be used to confine quantum systems in specially designed configurations. This generalizes a previous work where such energy barriers arose from flux lines with half-integer fluxons. Furthermore, it is shown how the Landau levels can be obtained from a two-dimensional grid of flux lines. These results suggest that the classical magnetic force can be seen as emerging entirely from the Aharonov-Bohm effect. Finally, the basic elements of a semiclassical theory that models the emergence of classical magnetic forces from fields with special symmetries are introduced.
Paiva, I.L., Aharonov, Y., Tollaksen, J., Waegell, M., 2020. Magnetic forces in the absence of a classical magnetic field. Physical Review A 101. https://doi.org/10.1103/PhysRevA.101.042111
American Physical Society