Magnetic forces in the absence of a classical magnetic field

I. L. Paiva, Y. Aharonov, J. Tollaksen, M. Waegell

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Article number042111
JournalPhysical Review A
Issue number4
StatePublished - Apr 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020 American Physical Society.


This work was partially supported by the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust. I.L.P. acknowledges financial support from the Science without Borders Program (CNPq/Brazil, Fund No. 234347/2014-7). Y.A. acknowledges support from the Israel Science Foundation (Grant 1311/14), Israeli Centers of Research Excellence (ICORE) Center “Circle of Light,” and DIP, the German-Israeli Project Cooperation.

FundersFunder number
Fetzer Franklin Fund of the John E. Fetzer Memorial Trust
Israel Science Foundation1311/14
Israeli Centers for Research Excellence


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