Few-Body Systems

, Volume 38, Issue 2–4, pp 147–152 | Cite as

Level Density of the Hénon-Heiles System Above the Critical Barrier Energy

  • M. Brack
  • J. Kaidel
  • P. Winkler
  • S. N. Fedotkin
Article
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Abstract.

We discuss the coarse-grained level density of the Hénon-Heiles system above the barrier energy, where the system is nearly chaotic. We use periodic orbit theory to approximate its oscillating part semiclassically via Gutzwiller’s semiclassical trace formula (extended by uniform approximations for the contributions of bifurcating orbits). Including only a few stable and unstable orbits, we reproduce the quantum-mechanical density of states very accurately. We also present a perturbative calculation of the stabilities of two infinite series of orbits (R n and L m ), emanating from the shortest librating straight-line orbit (A) in a bifurcation cascade just below the barrier, which at the barrier have two common asymptotic Lyapunov exponents χ R and χ L .

Keywords

Periodic Orbit Lyapunov Exponent Level Density Trace Formula Maslov Index 
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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • M. Brack
    • 1
  • J. Kaidel
    • 1
  • P. Winkler
    • 2
  • S. N. Fedotkin
    • 1
    • 3
  1. 1.Institut für Theoretische Physik, Universität RegensburgRegensburgGermany
  2. 2.Department of PhysicsUniversity of NevadaRenoUSA
  3. 3.Institute for Nuclear ResearchKiev-28Ukraine

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