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Fermi acceleration on the annular billiard.

R Egydio de Carvalho1, F Caetano Souza, Edson D Leonel

  • 1Departamento de Estatística, Matemática Aplicada e Computação, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, UNESP, Avenida 24A, 1515-Bela Vista, 13506-700, Rio Claro, São Paulo, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 16, 2006
PubMed
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Classical particles in annular billiards can achieve unlimited energy growth. Introducing time-dependent perturbations enables Fermi acceleration, even with periodic boundary oscillations, revealing new energy dynamics.

Area of Science:

  • Classical mechanics
  • Dynamical systems
  • Nonlinear dynamics

Background:

  • The annular billiard model explores particle dynamics in confined spaces.
  • Unlimited energy growth is a theoretical possibility in certain classical systems.
  • Fermi acceleration is a mechanism for particle energy increase through interaction with moving boundaries.

Purpose of the Study:

  • To investigate unlimited energy growth in a classical particle within an annular billiard.
  • To analyze the impact of static versus time-dependent (breathing) boundaries on particle energy.
  • To determine if Fermi acceleration can be induced under specific perturbed conditions.

Main Methods:

  • Simulations of a classical particle's trajectory in an annular billiard.

Related Experiment Videos

  • Analysis of system dynamics under static boundary conditions.
  • Introduction of periodic time-dependent perturbations to the boundaries.

    • Main Results:

    • Chaotic dynamics were observed in the static boundary case.
    • The introduction of time-dependent perturbations enabled Fermi acceleration.
    • Unlimited energy growth was demonstrated even when boundary oscillations were periodic.

    Conclusions:

    • Time-dependent boundary perturbations are key to inducing Fermi acceleration in this system.
    • The annular billiard model exhibits rich dynamics, allowing for energy gain under specific conditions.
    • This study highlights the potential for engineered systems to achieve particle energy amplification.