Fig. 3
From: Asymmetry and non-dispersivity in the Aharonov-Bohm effect
Dispersivity theorem and quantum “force”. The AB physical system, which involves the passage of electrons (blue) by an area of magnetic flux ΦB (gray circle), is analyzed in two ways. In case (1), the effect on a transversely-localized wavepacket with a longitudinal, Gaussian momentum distribution, \(e^{ - \left( {k_{\mathrm{L}} - k_{{\mathrm{L}}0}} \right)^2a^2/2}\), yields Zeilinger’s dispersivity theorem, implying the absence of forces that can lead to time delays. In case (2), the effect on a transverse, Gaussian position distribution yields Shelankov’s result to reveal the presence of a quantum “force” that leads to transverse deflection. Note that in both cases the electron wave never penetrates the area of magnetic flux. In physical realizations, the material that supports the magnetic flux area blocks the electron wave
