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

TL;DR

This paper investigates spectral singularities in a non-Hermitian extension of the Friedrichs-Fano-Anderson model, revealing their effects on reflection probabilities and state decay in a lattice system.

Contribution

It introduces a physical realization of spectral singularities in a non-Hermitian lattice model with boundary impurities, linking them to observable transport phenomena.

Findings

Spectral singularities cause diverging or vanishing reflection probabilities.

They prevent decay of the discrete state despite no bound states.

The model connects spectral singularities to physical transport properties.

Abstract

Spectral singularities are predicted to occur in a non-Hermitian extension of the Friedrichs-Fano-Anderson model describing the decay of a discrete state $|a >$ 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 non-decay of state $|a>$ into the continuum, in spite of the absence of bound states.