Rainbow Transition in Chaotic Scattering

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6 Citations (Scopus)


We study the effects of classical chaotic scattering on the differential cross section, which is the measurable quantity in most scattering experiments. We show that the fractal set of singularities in the deflection function is not, in general, reflected on the differential cross section. We show that there are systems in which, as the energy (or some other parameter) crosses a critical value, the system's differential cross-section changes from a singular function having an infinite set of rainbow singularities with structure in all scales to a smooth function with no singularities, the scattering being chaotic on both sides of the transition. We call this metamorphosis the rainbow transition. We exemplify this transition with a physically relevant class of systems. These results have important consequences for the problem of inverse scattering in chaotic systems and for the experimental observation of chaotic scattering.

Original languageEnglish
Article number035206
Number of pages4
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number3
Publication statusPublished - Mar 2002


  • cross-section
  • collisions
  • particles
  • cylinder
  • flows


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