Interference effects in an Aharonov-Bohm ring with random quantum dots

We investigate electron transport through quantum dots embedded in an Aharonov-Bohm ring. One or both of the dots are chaotic and are treated by random matrix theory. The conductance and conductance fluctuations are calculated as a function of the ratio of the level broadening to the average level spacing in the random dots using random scattering matrix theory with a Poisson kernel. Several interference mechanisms in the ring are examined. When one random dot and a single resonance level coexist and the multiple reflection between them is taken into account, the conductance is suppressed as the Fermi level of the leads approaches resonance in the large level broadening regime. For coupled random dot systems, characterized by two different ratios, the conductance is sensitive to the difference between the ratios when the multiple scattering inside the ring is disregarded, while it does not depend on the difference when the scattering is effective.