Non-Hermitian degeneracy of two unbound states

Abstract

We solved numerically the implicit, trascendental equation that defines the eigenenergy surface of a degenerating isolated doublet of unbound states in the simple but illustrative case of the scattering of a beam of particles by a double barrier potential. Unfolding the degeneracy point with the help of a contact equivalent approximant, crossings and anticrossings of energies and widths, as well as the changes of identity of the poles of the S-matrix are explained in terms of sections of the eigenenergy surfaces.

23 pages, 9 figures. To be published in J. of Physics A: Math. and Gen. Special issue: Pseudo-Hermitian Hamiltonians in Quantum Physics, August 2006