Rainbow Transition in Chaotic Scattering

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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
Volume65
Issue number3
DOIs
Publication statusPublished - Mar 2002

Fingerprint

rainbows
Scattering
Cross section
Singularity
scattering
cross sections
Fractal Set
Singular Functions
Inverse Scattering
inverse scattering
Smooth function
Differential System
Deflection
Chaotic System
Critical value
deflection
fractals
Energy
Experiment
energy

Keywords

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

Cite this

Rainbow Transition in Chaotic Scattering. / de Moura, A P S ; Grebogi, C .

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 65, No. 3, 035206, 03.2002.

Research output: Contribution to journalArticle

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