Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Triangle map: A model of quantum chaos

Casati1, Prosen

  • 1International Center for the Study of Dynamical Systems, Universita'degli Studi dell'Insubria, via Lucini, 3, I-22100 Como, Italy and and Istituto Nazionale di Fisica della Materia and INFN, Unita di Milano, Milano, Italy.

Physical Review Letters
|November 4, 2000
PubMed
Summary

This study numerically demonstrates that an area-preserving parabolic map, derived from billiard dynamics in an elongated triangle, exhibits ergodic and mixing properties. The particle motion on a cylinder follows a Gaussian diffusive process.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A reply

European journal of anaesthesiology·2000
Same author

Quantum resonances and regularity islands in quantum maps

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2000
Same author

Momentum conservation implies anomalous energy transport in 1D classical lattices

Physical review letters·2000
Same author

Quantum resonances of the kicked rotor and the SU(q) group

Physical review letters·2000
Same author

Fractal survival probability fluctuations

Physical review letters·2000
Same author

Quantization of a billiard model for interacting particles

Physical review letters·2000

Area of Science:

  • * Dynamical Systems
  • * Mathematical Physics
  • * Ergodic Theory

Background:

  • * The study of billiard systems provides insights into classical mechanics and chaos.
  • * Poincaré maps are essential tools for analyzing the long-term behavior of dynamical systems.
  • * Area-preserving maps are fundamental in Hamiltonian mechanics and celestial dynamics.

Purpose of the Study:

  • * To investigate the dynamical properties of an area-preserving parabolic map derived from a specific billiard problem.
  • * To provide numerical evidence for ergodicity and mixing in this map.
  • * To analyze the diffusive behavior of the system when extended to a cylindrical manifold.

Main Methods:

  • * Numerical simulations were employed to track the trajectories of a billiard particle within an elongated triangular boundary.

Related Experiment Videos

  • * The Poincaré map was constructed to represent the discrete dynamics of the system.
  • * Statistical analysis of particle trajectories was performed to assess ergodicity, mixing, and diffusive properties.

    • Main Results:

    • * Numerical evidence strongly suggests that the parabolic map is ergodic and mixing.
    • * The system exhibits chaotic behavior consistent with these properties.
    • * When analyzed on a cylinder, the particle's motion was found to approximate a Gaussian diffusive process.

    Conclusions:

    • * The area-preserving parabolic map derived from the elongated triangle billiard demonstrates complex dynamical behaviors.
    • * The findings support the theoretical understanding of ergodicity and mixing in such systems.
    • * The observed Gaussian diffusion on the cylinder suggests potential connections to statistical mechanics and transport phenomena.