Level Density of the Hénon-Heiles System Above the Critical Barrier Energy |
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Authors: | M Brack J Kaidel P Winkler S N Fedotkin |
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Institution: | Institut für Theoretische Physik, Universit?t Regensburg, D-93040, Regensburg, Germany Department of Physics, University of Nevada, 89557, Reno, NV, USA Institute for Nuclear Research, Prospekt Nauki 47, 252028, Kiev-28, Ukraine
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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 (Rn and Lm), 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 χR and χL. |
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