Level repulsion in the complex plane

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Abstract
We consider the spectral properties of a model quantum system describing 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 bound and continuum states (trapping effect) leading at high coupling to the formation of two time scales in terms of the lifetimes of the resonance states. In particular, we give a detailed analysis of the critical region where the system finds its new resonance structure. Eigenvalues, eigenfunctions, and their degree of mixing in relation to the corresponding wave functions of the closed system, as well as cross sections, are studied analytically and numerically for the cases of two and four resonances. For a multiresonance case the 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 redistributions acting on an energy scale comparable to the widths of the interfering resonances. (c) 1995 The American Physical Society