  We present results of a numerical experiment in which a neutral spin-1/2
particle subjected to a static magnetic vortex field passes through a
double-slit barrier. We demonstrate that the resulting interference pattern on
a detection screen exhibits fringes reminiscent of Aharonov-Bohm scattering by
a magnetic flux tube. To gain better understanding of the observed behavior, we
provide analytic solutions for a neutral spin-1/2 rigid planar rotor in the
aforementioned magnetic field. We demonstrate how that system exhibits a
non-Abelian Aharonov-Bohm effect due to the emergence of an effective Wu-Yang
(WY)flux tube. We study the behavior of the gauge invariant partition function
and demonstrate a topological phase transition for the spin-1/2 planar rotor.
We provide an expression for the partition function in which its dependence on
the Wilson loop integral of the WY gauge potential is explicit. We generalize
to a spin-1 system in order to explore the Wilzcek-Zee (WZ) mechanism in a full
quantum setting. We show how degeneracy can be lifted by higher order gauge
corrections that alter the semi-classical, non-Abelian, WZ phase. Models that
allow analytic description offer a foil to objections that question the
fidelity of predictions based on the generalized Born-Oppenheimer approximation
in atomic and molecular systems.
  Though the primary focus of this study concerns the emergence of gauge
structure in neutral systems, the theory is also applicable to systems that
posses electric charge. In that case, we explore interference between
fundamental gauge fields (i.e. electromagnetism) with effective gauge
potentials. We propose a possible laboratory demonstration for the latter in an
ion trap setting. We illustrate how effective gauge potentials influence
wave-packet revivals in the said ion trap.
