Avoided overlap between two resonance energies or frequencies: formation of fast and slow decay modes

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Abstract
The avoided overlap, i.e. the formation of fast and slow decay modes in open systems, is studied in a two-level model and generalized for the multidimensional case. The diagonalization regimes of two-dimensional non-Hermitian complex symmetric matrices H-i Gamma are defined as a function of a strength parameter chi and of the relative orientation S in the complex plane of the zero-order metastable states. In a multidimensional case, the X parameter corresponds to a matrix of binary parameters chi ij that accurately estimates the overlap. The definition of chi comes from the first-order complex correction on the eigenvectors, in the wave operator formalism. It provides a decoupling criterion, aiming at choosing the size of the effective complex matrix describing a bunch of resonances in a given energy range. The reorganization of the widths is exemplified in a vibrational predissociation, for an effective Hamiltonian, and in the exchange process in NMR spectroscopy, for an effective Liouvillian. In the first example, the eigenvectors corresponding to different canonical basis sets diabatic, and adiabatic representations, eigenvectors of H and Gamma are computed.

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