caa a22 4500 463197135 CHVBK 20180406164926.0 cr unu---uuuuu 170326e20070801xx s 000 0 eng 10.1007/s10773-006-9326-6 doi (NATIONALLICENCE)springer-10.1007/s10773-006-9326-6 Crossings and Anticrossings of Unbound States [Elektronische Daten] [E. Hernández, A. Jáuregui, A. Mondragón] We investigate the characteristic crossings and anticrossings of energies and widths of a doublet of resonances, observed in the vicinity of, and at a degeneracy of unbound states, when the control parameters of the system are varied. This characteristic behavior is explained in terms of the local, topological structure of the surfaces that represent the complex energy eigenvalues in parameter space in the vicinity of a degeneracy point. In the simple but illustrative case of the scattering of a beam of particles by a double barrier potential well with two regions of trapping, we solved numerically the implicit, transcendental equation that defines the eigenwave numbers of a degenerate isolated doublet of resonances as functions of the real, control parameters of the system. We found that, at a degeneracy of unbound states, the surface representing the resonance eigenwave numbers as functions of the control parameters has an algebraic branch point of rank one. Unfolding the degeneracy point, crossings and anticrossings of energies and widths are obtained as projections of sections of the eigenwave number surfaces. Springer Science+Business Media, LLC, 2007 multiple resonances nationallicence resonances nationallicence scattering theory nationallicence phases nationallicence geometric nationallicence dynamic or topological nationallicence Hernández E. Instituto de Física, UNAM, 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, UNAM, Apdo, Postal 20-364, 01000, México D.F., México aut International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/8(2007-08-01), 1890-1913 0020-7748 46:8<1890 2007 46 10773 https://doi.org/10.1007/s10773-006-9326-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-006-9326-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hernández E. Instituto de Física, UNAM, 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, UNAM, Apdo, Postal 20-364, 01000, México D.F., México aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/8(2007-08-01), 1890-1913 0020-7748 46:8<1890 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer