Spectral singularities in a non-Hermitian Friedrichs-Fano-Anderson model

Spectral singularities are predicted to occur in a non-Hermitian extension of the Friedrichs-Fano-Anderson model describing the decay of a discrete state vertical bar a > coupled to a continuum of modes. A physical realization of the model, based on electronic or photonic transport in a semi-infinite tight-binding lattice with an imaginary impurity site at the lattice boundary, is proposed. The occurrence of the spectral singularities is shown to correspond either to a diverging reflection probability (for an amplifying impurity) or to a vanishing reflection probability (for an absorbing impurity) from the lattice boundary. In the former case, the spectral singularity of the resolvent is also responsible for the nondecay of state vertical bar a > into the continuum, in spite of the absence of bound states.