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.

arXiv comment23 pages, 9 figures. To be published in J. of Physics A: Math. and Gen. Special issue: Pseudo-Hermitian Hamiltonians in Quantum Physics, August 2006

References in corpus (16)

• Exceptional Points of Non-hermitian Operators
• PT -symmetric harmonic oscillators
• Observation of a Chiral State in a Microwave Cavity
• Geometric phase around exceptional points
• Observation of Exceptional Points in Electronic Circuits
• Phases of Wave Functions and Level Repulsion
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• Spontaneous breakdown of PT symmetry in the solvable square-well model
• Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation
• Berry Phase of a Resonant State
• Jordan blocks and Gamow-Jordan eigenfunctions associated to a double pole of the S-matrix
• Gamow-Jordan Vectors and Non-Reducible Density Operators from Higher Order S-Matrix Poles
• Coupled-channel version of PT-symmetric square well
• Interference of resonances and the double-pole of the S-matrix in a double well system
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