  We theoretically study the propagation of a guided atom laser across an
Aharonov-Bohm ring which is exposed to a synthetic gauge field. The presence of
disorder within the ring gives rise to Al'tshuler-Aronov-Spivak oscillations,
seen in the disorder average of the transmission as a function of the effective
gauge flux that is contained within the ring. Those oscillations are induced by
coherent backscattering and represent a manifestation of weak localization.
Through analytical and numerical calculations that are based on the mean-field
Gross-Pitaevskii approximation for the propagating Bose-Einstein condensate, we
show that the presence of a very weak atom-atom interaction within the ring
leads to an inversion of the Al'tshuler-Aronov-Spivak oscillations, in a very
similar manner as for the coherent backscattering of Bose-Einstein condensates
within two-dimensional disorder potentials. Numerical simulations based on the
Truncated Wigner method reveal that this signature of weak antilocalization
becomes washed out if the interaction strength is increased.
