Level density of the Hénon-Heiles system above the critical barrier Energy

Details Level density of the Hénon-Heiles system above the critical barrier Energy Level density of the Hénon-Heiles system above the critical barrier Energy

2005-11-02

arxiv.org/abs/nlin/0511005v2

Few Body Systems 38 (2006) pp. 147 - 152

Nonlinear Sciences

Chaotic Dynamics

LaTeX, style FBS (Few-Body Systems), 6pp. 2 Figures; invited talk at "Critical stability of few-body quantum systems", MPI-PKS

Scientific paper

10.1007/s00601-005-0124-0

We discuss the coarse-grained level density of the H\'enon-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 $\chi_{\rm R}$ and $\chi_{\rm L}$.

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