The Aharonov-Bohm effect as a manifestation of the Zeeman interaction

Simon N. M. Ruijsenaars

Keith J. Kasunic

The Aharonov-Bohm (AB) effect is now largely considered to be a manifestation of geometric phase. However, by decomposing the vector-potential gradient tensor into divergence, curl, and shear components, we isolate a field/charged-particle interaction that is not dependent on local electric and magnetic fields. We show that a local shear field provides a velocity-dependent, dynamic-phase interaction in the AB effect whose predictions are consistent with all known classes of AB experiments, including interference fringe shifts, the absence of time delays along the direction of propagation, and the possibility of lateral forces.

Vladimir D. Skarzhinsky

Tomislav Ivezić

In this paper it is presented a manifestly covariant formulation of the Aharonov-Bohm (AB) phase difference for the magnetic AB effect. This covariant AB phase is written in terms of the Faraday 2-form F and using the decomposition of F in terms of the electric and magnetic fields as four-dimensional (4D) geometric quantities. It is shown that there is a static electric field outside a stationary solenoid with resistive conductor carrying steady current, which causes that the AB phase difference in the magnetic AB effect may be determined by the electric part of the covariant expression, i.e., by the local influence of the 4D electric field and not, as generally accepted, in terms of nonzero vector potential.

Chris Philippidis, David Böhm, R.D. Kaye

Erik Sjöqvist, Martin Almquist, Ken Roger Mattsson +2 more

The adiabatic Aharonov-Bohm (AB) effect is a manifestation of the Berry phase acquired when some slow variables take a planar spin around a loop. While the effect has been observed in molecular spectroscopy, direct measurement of the topological phase shift in a scattering experiment has been elusive in the past. Here, we demonstrate an adiabatic AB effect by explicit simulation of the dynamics of unpolarized very slow neutrons that scatter on a long straight current-carrying wire.