Transition from isolated to overlapping resonances in the open system of interacting fermions

We study the statistical properties of resonance widths and spacings in an open system of interacting fermions. At the transition between isolated and overlapping resonances, a radical change in the width distribution occurs with segregation of broad ("super-radiant") and narrow ("trapped") states. Our main interest is to reveal how this transition is influenced by the onset of chaos in the internal dynamics regulated by the strength of random two-body interaction. In the transitional region, the width distribution and its variance, as well as the distribution of spacings between resonances are strongly affected by internal chaos. The results may be applied to the analysis of neutron cross sections, as well as in the physics of mesoscopic devices with strongly interacting electrons.