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Kaidel J, Winkler P, Brack M. Periodic orbit theory for the Hénon-Heiles system in the continuum region. Phys Rev E Stat Nonlin Soft Matter Phys. 2004;70(6):066208doi: 10.1103/PhysRevE.70.066208.
Kaidel, J., Winkler, P., & Brack, M. (2004). Periodic orbit theory for the Hénon-Heiles system in the continuum region. Physical review. E, Statistical, nonlinear, and soft matter physics, 70(6), 066208. https://doi.org/10.1103/PhysRevE.70.066208
Kaidel, J, et al. "Periodic orbit theory for the Hénon-Heiles system in the continuum region." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 70,6 (2004): 066208. doi: https://doi.org/10.1103/PhysRevE.70.066208
Kaidel J, Winkler P, Brack M. Periodic orbit theory for the Hénon-Heiles system in the continuum region. Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Dec;70(6):066208. doi: 10.1103/PhysRevE.70.066208. Epub 2004 Dec 16. PMID: 15697485.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Dec;70(6):066208. doi: 10.1103/PhysRevE.70.066208. Epub 2004 Dec 16.

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

Physical review. E, Statistical, nonlinear, and soft matter physics

J Kaidel, P Winkler, M Brack

Affiliations

  1. Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany.

PMID: 15697485 DOI: 10.1103/PhysRevE.70.066208

Abstract

We investigate the resonance spectrum of the Hénon-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 co-dimension-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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