  The Aharanov-Bohm (AB) effect, which predicts that a magnetic field strongly
influences the wave function of an electrically charged particle, is
investigated in a three site system in terms of the quantum control by an
additional dephasing source. The AB effect leads to a non-monotonic dependence
of the steady-state current on the gauge phase associated with the molecular
ring. This dependence is sensitive to site energy, temperature, and dephasing,
and can be explained using the concept of the dark state. Although the phase
effect vanishes in the steady-state current for strong dephasing, the phase
dependence remains visible in an associated waiting-time distribution,
especially at short times. Interestingly, the phase rigidity (i.e., the
symmetry of the AB phase) observed in the steady-state current is now broken in
the waiting-time statistics, which can be explained by the interference between
transfer pathways.
