Level repulsion in the complex plane

We consider the spectral properties of a model quantum system deseribing the coupling of bound states to a number of decay channels. We describe the separation of a few modes from the Set of all resonances during the transition from low to high coupling strength between bonnd and continunm states (irapping etfect) leading at high wnpling to the formation of two time scales in terms of the life times of the resonance states. In particular, we give a detailed analysis of the critical region where the system finds its new resonance structure. Eigenvalues, eigenfnnctions and their degree of mixing in relation to the corresponding wavefunctions of the closed system as weil as Cross sections are stndied analytically and numerically for the cFes of two and four resonances. For a multi-resonance case tbe dependence of these quantities on the spectrum of the underlying closed system is studied. We find that the global reorganization of the spectrum in the high coupling regime can be traced back to local redistribntions acting on an energy scale comparable to the widths of the interfering resonances. PACS: 03.65.Nk, 05.30.-d, 05.40.+j, 24.60.-k