Kaidel, Joerg and Brack, Matthias (2004) Semiclassical trace formulas for pitchfork bifurcation sequences. PHYSICAL REVIEW E, 70 (1): 016206. ISSN 1539-3755,
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In nonintegrable Hamiltonian systems with mixed phase space and discrete symmetries, sequences of pitchfork bifurcations of periodic orbits pave the way from integrability to chaos. In extending the semiclassical trace formula for the spectral density, we develop a uniform approximation for the combined contribution of pitchfork bifurcation pairs. For a two-dimensional double-well potential and the familiar Henon-Heiles potential, we obtain very good agreement with exact quantum-mechanical calculations. We also consider the integrable limit of the scenario which corresponds to the bifurcation of a torus from an isolated periodic orbit. For the separable version of the Henon-Heiles system we give an analytical uniform trace formula, which also yields the correct harmonic-oscillator SU(2) limit at low energies, and obtain excellent agreement with the slightly coarse-grained quantum-mechanical density of states.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PERIODIC-ORBITS; HAMILTONIAN-SYSTEMS; UNIFORM APPROXIMATION; DEFORMED-NUCLEI; BOUND SPECTRUM; QUANTUM BEATS; CLOSED ORBITS; SYMMETRY; POTENTIALS; MECHANICS; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Alumni or Retired Professors > Group Matthias Brack |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 12 Jul 2021 09:41 |
| Last Modified: | 12 Jul 2021 09:41 |
| URI: | https://pred.uni-regensburg.de/id/eprint/37516 |
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