  We study the chaotic scattering through an Aharonov-Bohm ring containing two
cavities. One of the cavities has well-separated resonant levels while the
other is chaotic, and is treated by random matrix theory. The conductance
through the ring is calculated analytically using the supersymmetry method and
the quantum fluctuation effects are numerically investigated in detail. We find
that the conductance is determined by the competition between the mean and
fluctuation parts. The dephasing effect acts on the fluctuation part only. The
Breit-Wigner resonant peak is changed to an antiresonance by increasing the
ratio of the level broadening to the mean level spacing of the random cavity,
and the asymmetric Fano form turns into a symmetric one. For the orthogonal and
symplectic ensembles, the period of the Aharonov-Bohm oscillations is half of
that for regular systems. The conductance distribution function becomes
independent of the ensembles at the resonant point, which can be understood by
the mode-locking mechanism. We also discuss the relation of our results to the
random walk problem.
