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

Gross-Pitaevski map as a chaotic dynamical system.

Italo Guarneri1

  • 1Center for Nonlinear and Complex Systems, Dipartimento di Scienza ed Alta Tecnologia, Universitá dell'Insubria, via Valleggio 11, I-22100 Como, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, via Bassi 6, I-27100 Pavia, Italy.

Physical Review. E
|April 19, 2017
PubMed
Summary
This summary is machine-generated.

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

Classical dynamical localization.

Physical review letters·2014
Same author

Exponential quantum spreading in a class of kicked rotor systems near high-order resonances.

Physical review. E, Statistical, nonlinear, and soft matter physics·2013
Same author

Fidelity for kicked atoms with gravity near a quantum resonance.

Physical review. E, Statistical, nonlinear, and soft matter physics·2012
Same author

Classical dynamics of quantum entanglement.

Physical review. E, Statistical, nonlinear, and soft matter physics·2012
Same author

Long-lasting exponential spreading in periodically driven quantum systems.

Physical review letters·2011
Same author

Pseudoclassical theory for fidelity of nearly resonant quantum rotors.

Physical review. E, Statistical, nonlinear, and soft matter physics·2009

The Gross-Pitaevskii map exhibits chaotic dynamics and exponential energy growth due to rotational invariance. Analysis reveals an integrable-chaotic transition in resonant cases.

Area of Science:

  • Mathematical Physics
  • Dynamical Systems Theory
  • Nonlinear Dynamics

Background:

  • The Gross-Pitaevskii equation describes Bose-Einstein condensates.
  • A discrete-time version, the Gross-Pitaevskii map, has shown exponential instability.
  • This study treats the map as a classical dynamical system.

Purpose of the Study:

  • To systematically analyze the chaotic behavior of the Gross-Pitaevskii map.
  • To investigate the relationship between rotational invariance and energy growth.
  • To compute the Lyapunov spectrum for stationary solutions, including resonant cases.

Main Methods:

  • Analysis of Lyapunov exponents to quantify chaotic behavior.
  • Analytical computation of the full Lyapunov spectrum for stationary solutions.

Related Experiment Videos

  • Inclusion of the resonant case where the free rotation period is commensurate to 2π.

    • Main Results:

    • Strongly chaotic behavior was exposed through Lyapunov exponent analysis.
    • Exponential energy growth was directly linked to rotational invariance.
    • Countably many constants of motion exist in the resonant case.
    • An integrable-chaotic transition was observed, except for lowest-order resonances.

    Conclusions:

    • The Gross-Pitaevskii map demonstrates complex dynamics, including chaos and instability.
    • Rotational invariance is a key factor driving exponential energy growth.
    • The system exhibits a transition from integrable to chaotic behavior under specific resonant conditions.