caa a22 4500 463195582 CHVBK 20180406164921.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s10773-006-9325-7 doi (NATIONALLICENCE)springer-10.1007/s10773-006-9325-7 Degeneracy of Resonances: Branch Point and Branch Cuts in Parameter Space [Elektronische Daten] [E. Hernández, A. Jáuregui, A Mondragón, L. Nellen] The rich phenomenology of crossings and anticrossings of energies and widths, observed in an isolated doublet of resonances when one control parameter is varied, is fully explained in terms of the topological properties of the energy hypersurfaces close to the degeneracy point. The hypersurface representing the complex resonance eigenvalues, as functions of the control parameters, has an algebraic branch point of rank one, and branch cuts in its real and imaginary parts, 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 any 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. Springer Science+Business Media, LLC, 2007 multiple resonances degeneracies nationallicence non-relativistic scattering theory phases: topological nationallicence Berry phase nationallicence Hernández E. Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, México D.F., México aut Jáuregui A. Departamento de Física, Universidad de Sonora, Apdo. Postal 1626, Hermosillo, Sonora, México aut Mondragón A. Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, México D.F., México aut Nellen L. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, 04510, México D.F., México aut International Journal of Theoretical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 46/6(2007-06-01), 1666-1701 0020-7748 46:6<1666 2007 46 10773 https://doi.org/10.1007/s10773-006-9325-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-006-9325-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hernández E. Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, México D.F., México aut NATIONALLICENCE 700 1- Jáuregui A. Departamento de Física, Universidad de Sonora, Apdo. Postal 1626, Hermosillo, Sonora, México aut NATIONALLICENCE 700 1- Mondragón A. Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, México D.F., México aut NATIONALLICENCE 700 1- Nellen L. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, 04510, México D.F., México aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 46/6(2007-06-01), 1666-1701 0020-7748 46:6<1666 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer