Non-Hermitian effective Hamiltonian approach to Open Quantum Systems: Statistical properties of cross sections.

We will briefly present the Non-Hermitian effective Hamiltonian approach to Open Quantum Systems. This approach, based on the Feshbach formalism, allows to take into account the coupling of a finite number of discrete states with a continuum through an effective non-hermitian hamiltonian. It is well known that, at a critical value of the coupling with the continuum, a redistribution of the resonance widths occurs. In fact, some states acquire a broad width, similarly to superrandiant states, whereas for others the width becomes very small. In particular the effect of the widths reditribution on the statistical properties of the cross section is considered.Comparison with prediction of Ericson in the overlapping resonance regime are made. Statistical properties of cross section are also studied for different ensemble describing the dynamics of a quantum system interacting with the continuum.