Avoided level crossings in open quantum systems
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Openquantum system,levelcrossing, exceptional point,overlapping resonances, complexcoupling between system and environment, width bifurcation. At high level density, two states avoid usually crossing at the critical value acr of the parameter a by which the system is controlled. The wavefunctions of the two states are mixed in a ﬁnite parameter range around acr. This holds true for discrete states as well as for narrow resonance states which are coupled via the environment of scattering wavefunctions. We study the inﬂuence of avoided level crossings onto four overlapping complex eigenvalues of a symmetric non-Hermitian operator. The mixing of the two wavefunctions around acr issimulated, ineach case, byassuming a Gaussian distributionaround acr.At highlevel density, the Gaussian distributions related to avoided crossings of different levels may overlap. Here, new effects arise, especially from the imaginary part of the coupling term via the environment. The results show, moreover, the inﬂuence of symmetries onto the multi-level avoided crossing phenomenon.