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

Semiclassical trace formulas for pitchfork bifurcation sequences.

J Kaidel1, M Brack

  • 1Institute for Theoretical Physics, University of Regensburg, D-93040 Regensburg, Germany. joerg.kaidel@physik.uni-regensburg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 25, 2004
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

Pre-infection of pigs with Mycoplasma hyopneumoniae induces oxidative stress that influences outcomes of a subsequent infection with a swine influenza virus of H1N1 subtype.

Veterinary microbiology·2012
Same author

[Oxidative stress and fertility: false evidence and bad recipes].

Gynecologie, obstetrique & fertilite·2012
Same author

Semiclassical theory for spatial density oscillations in fermionic systems.

Physical review. E, Statistical, nonlinear, and soft matter physics·2010
Same author

A machine-learning approach to the prediction of oxidative stress in chronic inflammatory disease.

Redox report : communications in free radical research·2009
Same author

Periodic orbit theory for the Hénon-Heiles system in the continuum region.

Physical review. E, Statistical, nonlinear, and soft matter physics·2005
Same author

Semiclassical theory of spin-orbit interactions using spin coherent states.

Physical review letters·2002
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

Researchers developed a uniform approximation for Hamiltonian systems, improving predictions of spectral density and chaos. This method accurately models pitchfork bifurcations in systems like the Hénon-Heiles potential, bridging classical and quantum mechanics.

Area of Science:

  • * Theoretical physics
  • * Quantum mechanics
  • * Dynamical systems

Background:

  • * Nonintegrable Hamiltonian systems with mixed phase space and discrete symmetries exhibit complex dynamics.
  • * Pitchfork bifurcations of periodic orbits are crucial in the transition from integrability to chaos.
  • * Understanding spectral density in these systems is key to characterizing their behavior.

Purpose of the Study:

  • * To develop a uniform approximation for the spectral density in systems with pitchfork bifurcations.
  • * To extend the semiclassical trace formula to include combined contributions of bifurcation pairs.
  • * To validate the approximation against quantum-mechanical calculations for specific potentials.

Main Methods:

  • * Extension of the semiclassical trace formula.

Related Experiment Videos

  • * Development of a uniform approximation for pitchfork bifurcation pairs.
  • * Application to two-dimensional double-well and Hénon-Heiles potentials.
  • * Analysis of the integrable limit and separable Hénon-Heiles system.

    • Main Results:

    • * Very good agreement between the uniform approximation and exact quantum-mechanical calculations for double-well and Hénon-Heiles potentials.
    • * Accurate modeling of the spectral density contributions from pitchfork bifurcation pairs.
    • * Excellent agreement with coarse-grained quantum-mechanical density of states for the separable Hénon-Heiles system.
    • * The analytical uniform trace formula correctly reproduces the harmonic-oscillator SU(2) limit.

    Conclusions:

    • * The developed uniform approximation provides a powerful tool for analyzing spectral densities in nonintegrable Hamiltonian systems.
    • * The method effectively captures the influence of pitchfork bifurcations on system dynamics and spectral properties.
    • * This work offers a unified approach to understanding the transition from integrability to chaos in complex systems.