Abstract
Applications of the generalized Dyson mapping lead to non-Hermitian Hamiltonians when they are expressed in the convenient space of independent bosons and fermions. We show how this formalism may be applied to the Richardson model which has recently been demonstrated to be appropriate for the description of superconducting metallic grains. For the first time a perturbative calculation of the wave function and a time-dependent analysis become possible, very much facilitated by a proper application of degenerate perturbation theory for non-Hermitian operators. We briefly discuss the implications for the description of ultra-cold Fermi gases which may also be described within the same framework.
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