Non-Hermitian N-state degeneracies: unitary realizations via antisymmetric anharmonicities

The phenomenon of degeneracy of an N-plet of bound states is studied in the framework of quantum theory of closed (i.e., unitary) systems. For an underlying Hamiltonian H=H(λ) the degeneracy occurs at a Kato's exceptional point λ^(EPN) of order N and of the spectral geometric multiplicity K<N. In spite of the phenomenological appeal of the concept (tractable as a quantum phase transition, or as a unitary processes of the loss of the observability of the system), the dedicated literature deals, predominantly, just with the models where N=2 and K=1. In our paper it is shown that the construction of the N>2 and K>1 benchmark models of the process of degeneracy becomes feasible and non-numerical for a broad class of specific, maximally non-Hermitian anharmonic-oscillator toy-model Hamiltonians. An exhaustive classification of non-equivalent processes is given by a partitioning of the unperturbed spectrum into equidistant and centered unperturbed subspectra.