Exceptional points and non-Hermitian degeneracy of resonances in a two-channel model

Abstract

We study the mixing and degeneracy of two unbound energy eigenstates (resonances) in a two coupled channel model of scattering and reactions. We derive the necessary and sufficient conditions for existence of an exceptional point in the extended spectrum of bound and resonance energy eigenvalues in this model and show that these are not the same as in the single channel case. When these conditions are satisfied, in the complex energy plane, the two simple resonance poles of the scattering matrix merge into one double pole at the exceptional point. In parameter space, the surface of the eigenenergies has a branch point of square root type and branch cuts in its real and imaginary parts that start at the exceptional point and extend in opposite directions. The rich phenomenology of crossings and anticrossings of energies and widths of the doublet of unbound states, as well as the changes of identity of the poles of the scattering matrix observed when one control parameter is varied while the other is kept constant, is fully explained in terms of sections of the eigenenergy surfaces.