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

Quantum chaos for the radially vibrating spherical billiard.

Richard L. Liboff1, Mason A. Porter

  • 1Schools of Electrical Engineering and Applied Physics and Center for Applied Mathematics, Cornell University, Ithaca, New York 14853.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
Summary

Quantum chaos arises in a spherical billiard only when superposition states possess common rotational symmetry. This study details nonchaotic and chaotic states, deriving Hamiltonians and motion equations for quantum systems with time-varying radii.

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

The Sinai billiard, square torus, and field chaos.

Chaos (Woodbury, N.Y.)·2003
See all related articles

Area of Science:

  • Quantum mechanics
  • Chaos theory
  • Mathematical physics

Background:

  • The behavior of quantum systems within confined spaces (billiards) is a key area of study.
  • Understanding the conditions under which quantum systems exhibit chaotic dynamics is crucial for various fields.

Purpose of the Study:

  • To investigate the conditions for chaos in a spherical quantum billiard with a time-dependent radius.
  • To characterize both nonchaotic and chaotic states within this system.

Main Methods:

  • Derivation of a Hamiltonian for the spherical quantum billiard with a time-varying radius, a(t).
  • Analysis of superposition states, focusing on those with common rotational symmetry.
  • Utilizing Bloch variables (x,y,z) to describe motion in the chaotic regime.

Related Experiment Videos

  • Introduction of a potential function to ensure bounded motion of the radius.
  • Employing Poincare maps and projections onto the Bloch sphere to identify chaotic characteristics.

    • Main Results:

    • Chaos is demonstrated to occur exclusively in superposition states with shared rotational symmetry.
    • A Hamiltonian is derived for both nonchaotic and chaotic scenarios, involving canonical coordinate 'a' and momentum 'P'.
    • Equations of motion are established for the chaotic case using Bloch variables.
    • Poincare maps and Bloch sphere projections confirm the presence of chaotic behavior.

    Conclusions:

    • The presence of common rotational symmetry in superposition states is the sole determinant of chaos in this spherical quantum billiard model.
    • The derived Hamiltonian and motion equations provide a framework for studying quantum chaos in systems with dynamic boundaries.