Geometrical theory of diffracted rays, orbiting and complex rays (Articolo in rivista)

Type
Label
  • Geometrical theory of diffracted rays, orbiting and complex rays (Articolo in rivista) (literal)
Anno
  • 2006-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1134/S1061920806030034 (literal)
Alternative label
  • De Micheli Enrico; Viano Giovanni Alberto (2006)
    Geometrical theory of diffracted rays, orbiting and complex rays
    in Russian journal of mathematical physics
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • De Micheli Enrico; Viano Giovanni Alberto (literal)
Pagina inizio
  • 253 (literal)
Pagina fine
  • 277 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://www.springerlink.com/content/046561772x409k05/ (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 13 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 3 (literal)
Note
  • Scopu (literal)
  • ISI Web of Science (WOS) (literal)
  • athematical Reviews on the web (MathSciNet) (literal)
  • Google Scholar (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Istituto di Biofisica, Consiglio Nazionale delle Ricerche, Genova, Italy - Dipartimento di Fisica, Universita' di Genova, Genova, Italy (literal)
Titolo
  • Geometrical theory of diffracted rays, orbiting and complex rays (literal)
Abstract
  • In this article, the ray tracing method is studied beyond the classical geometrical theory. The trajectories are here regarded as geodesics in a Riemannian manifold, whose metric and topological properties are those induced by the refractive index (or, equivalently, by the potential). First, we derive the geometrical quantization rule, which is relevant to describe the orbiting bound-states observed in molecular physics. Next, we derive properties of the diffractive rays, regarded here as geodesics in a Riemannian manifold with boundary. A particular attention is devoted to the following problems: (i) modification of the classical stationary phase method suited to a neighborhood of a caustic; (ii) derivation of the connection formulas which enable one to obtain the uniformization of the classical eikonal approximation by patching up geodesic segments crossing the axial caustic; (iii) extension of the eikonal equation to mixed hyperbolic-elliptic systems, and generation of complex-valued rays in the shadow of the caustic. By these methods, we can study creeping waves in diffractive scattering, describe the orbiting resonances present in molecular scattering beside the orbiting bound-states, and, finally, describe the generation of evanescent waves, which are relevant in the nuclear rainbow. (literal)
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