Fano resonances in the conductance of quantum dots with mixed dynamics

We study the conductance fluctuations of an open quantum dot with underlying mixed dynamics. In addition to smooth conductance fluctuations, typical of chaotic quantum dots, we observe the occurrence of many sharp conductance peaks. Those are associated with localized states in the quantum dot and display a variety of Fano shape resonances. We show that the Fano q parameter in the presence of time-reversal symmetry is, in general, complex. We discuss the origin of the different Fano parameters and present a numerical study to support our theory.