dorsal/arxiv
View SchemaUnfolding a degeneracy point of two unbound states: Crossings and anticrossings of energies and widths
| Authors | E. Hernandez, A. Jauregui, A. Mondragon, L. Nellen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0501124 |
| URL | https://arxiv.org/abs/quant-ph/0501124 |
Abstract
We show that when an isolated doublet of unbound states of a physical system becomes degenerate for some values of the control parameters of the system, the energy hypersurfaces representing the complex resonance energy eigenvalues as functions of the control parameters have an algebraic branch point of rank one in parameter space. Associated with this singularity in parameter space, the scattering matrix, S_l(E), and the Green's function, G_l^(+)(k; r,r'), have one double pole in the unphysical sheet of the complex energy plane. We characterize the universal unfolding or deformation of a typical degeneracy point of two unbound states in parameter space by means of a universal 2-parameter family of functions which is contact equivalent to the pole position function of the isolated doublet of resonances at the exceptional point and includes all small perturbations of the degeneracy condition up to contact equivalence.
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"date_created": "2026-03-02T18:02:13.038000Z",
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"abstract": "We show that when an isolated doublet of unbound states of a physical system\nbecomes degenerate for some values of the control parameters of the system, the\nenergy hypersurfaces representing the complex resonance energy eigenvalues as\nfunctions of the control parameters have an algebraic branch point of rank one\nin parameter space. Associated with this singularity in parameter space, the\nscattering matrix, S_l(E), and the Green\u0027s function, G_l^(+)(k; r,r\u0027), have one\ndouble pole in the unphysical sheet of the complex energy plane. We\ncharacterize the universal unfolding or deformation of a typical degeneracy\npoint of two unbound states in parameter space by means of a universal\n2-parameter family of functions which is contact equivalent to the pole\nposition function of the isolated doublet of resonances at the exceptional\npoint and includes all small perturbations of the degeneracy condition up to\ncontact equivalence.",
"arxiv_id": "quant-ph/0501124",
"authors": [
"E. Hernandez",
"A. Jauregui",
"A. Mondragon",
"L. Nellen"
],
"categories": [
"quant-ph"
],
"title": "Unfolding a degeneracy point of two unbound states: Crossings and anticrossings of energies and widths",
"url": "https://arxiv.org/abs/quant-ph/0501124"
},
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