Brack, Matthias and Fedotkin, S. N. and Magner, A. G. and Mehta, M. (2003) Analytical perturbative approach to periodic orbits in the homogeneous quartic oscillator potential. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 36 (4). pp. 1095-1110. ISSN 0305-4470
Full text not available from this repository.Abstract
We present an analytical calculation of periodic orbits in the homogeneous quartic oscillator potential. Exploiting the properties of the periodic Lame functions that describe the orbits bifurcated from the fundamental linear orbit in the vicinity of the bifurcation points, we use perturbation theory to obtain their evolution away from the bifurcation points. As an application, we derive an analytical semiclassical trace formula for the density of states in the separable case, using a uniform approximation for the pitchfork bifurcations occurring there, which allows for full semiclassical quantization. For the non-integrable situations, we show that the uniform contribution of the bifurcating period-one orbits to the coarse-grained density of states competes with that of the shortest isolated orbits, but decreases with increasing chaoticity parameter alpha.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GUTZWILLERS TRACE FORMULA; HAMILTONIAN-SYSTEMS; SPECTRAL STATISTICS; BIFURCATIONS; QUANTIZATION; EXPONENTS; |
| 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: | 24 Aug 2021 13:14 |
| Last Modified: | 24 Aug 2021 13:14 |
| URI: | https://pred.uni-regensburg.de/id/eprint/39342 |
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