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Multiple scattering by two impenetrable cylinders: semiclassical theory.

P Gabrielli1, M Mercier-Finidori

  • 1Equipe Ondes et Acoustique, CNRS UMR No. 6134, Faculté des Sciences, Université de Corse, Boîte Postal 52, 20250 Corte, France. gabrieli@univ-corse.fr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 22, 2002
PubMed
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This study analyzes wave and particle scattering by two parallel cylinders. Semiclassical methods reveal periodic orbits, showing excellent agreement between theoretical predictions and exact results for this canonical problem.

Area of Science:

  • Physics
  • Wave phenomena
  • Scattering theory

Background:

  • Understanding wave and particle interactions with geometric structures is fundamental in physics.
  • The scattering of waves by cylindrical objects is a well-established but complex problem.

Purpose of the Study:

  • To investigate the scattering of waves and particles by two identical, impenetrable, parallel cylinders.
  • To develop generalized formulas for geometrical and composite scattering contributions.
  • To interpret scattering resonances as periodic orbits and validate them against exact results.

Main Methods:

  • Expansion of the characteristic determinant of scattering matrices in terms of simple traces.
  • Semiclassical evaluation of these traces to extract periodic orbits.

Related Experiment Videos

  • Derivation of generalized formulas for scattering contributions.

    • Main Results:

    • Periodic orbits were successfully extracted using semiclassical evaluation.
    • Generalized formulas were derived for both purely geometrical and composite scattering.
    • Scattering resonances, interpreted as periodic orbits, showed excellent agreement with exact solutions.

    Conclusions:

    • The scattering of waves and particles by two impenetrable cylinders is a canonical problem in physics.
    • The semiclassical approach provides an accurate method for analyzing scattering phenomena.
    • The identified periodic orbits offer valuable insights into the underlying physics of wave-particle interactions.