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

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

2003-12-10

arxiv.org/abs/nlin/0312022v3

Phys. Rev. E 70, 066208 (2004) 8 pp.

Nonlinear Sciences

Chaotic Dynamics

LaTeX (v3): 10 pages, 9 figures (new figure 6 added), 1 table; final version for Phys. Rev. E (in print)

Scientific paper

10.1103/PhysRevE.70.066208

We investigate the resonance spectrum of the H\'enon-Heiles potential up to twice the barrier energy. The quantum spectrum is obtained by the method of complex coordinate rotation. We use periodic orbit theory to approximate the oscillating part of the resonance spectrum semiclassically and Strutinsky smoothing to obtain its smooth part. Although the system in this energy range is almost chaotic, it still contains stable periodic orbits. Using Gutzwiller's trace formula, complemented by a uniform approximation for a codimension-two bifurcation scenario, we are able to reproduce the coarse-grained quantum-mechanical density of states very accurately, including only a few stable and unstable orbits.

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