Bound states at exceptional points in the continuum

Abstract

In this work, an example of exceptional points in the continuous spectrum of a Hamiltonian of von Neumann-Wigner type is presented and discussed. Remarkably, these exceptional points are not associated with a double pole in the scattering matrix but with a double pole in the normalization factor of the Jost eigenfunctions normalized to unit flux. At the exceptional points the two unnormalized Jost eigenfunctions are no longer linearly independent but coalesce to give rise to two Jordan cycles of generalized bound state energy eigenfunctions in the continuum and a Jordan block representation of the Hamiltonian. The regular scattering eigenfunction vanishes at the exceptional points and the irregular scattering eigenfunction has a double pole at the exceptional points. The scattering matrix is a regular analytical function of the wave number k for all k real including the exceptional points.