  The Fano resonance in quantum dots embedded in Aharonov-Bohm rings is
examined theoretically, using two models of non-interacting electrons. The
first model yields an analytical expression for the conductance G. G is written
in an extended Fano form with a complex parameter. The shape of the resonance
can be asymmetric or symmetric, depending on the magnetic flux enclosed in the
ring. The "phase" of the resonance is changed continuously with increasing the
flux in two-terminal situations. These are in accordance with recent
experimental results. In the second model, we consider the dephasing effect on
the Fano resonance by numerical calculations.
