Brack, Matthias and Creagh, S. C. and Law, J. (1998) Level-density fluctuations at the bottom of a potential. PHYSICAL REVIEW A, 57 (2). pp. 788-797. ISSN 2469-9926, 2469-9934
Full text not available from this repository.Abstract
We evaluate trace formulas for various perturbations of two-dimensional harmonic oscillators. Such systems arise naturally in the expansion of generic potentials about local minima. For large enough perturbations the usual theory for isolated orbits applies and we can reproduce the long and medium-range oscillations in the density of states in terms of the shortest periodic orbits. For small perturbations, or low energies, the Gutzwiller amplitudes diverge due to the approaching degeneracy of the harmonic oscillator. We employ a perturbative analysis of the classical dynamics to give a treatment of the trace formula that is valid near the degenerate harmonic regime. First-order perturbation theory works for generic cases. For certain potentials, such as Henon-Heiles, discrete symmetries lead to a null result at first order and second-order calculations are necessary to capture the dominant features.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SEMICLASSICAL TRACE FORMULAS; ORBITAL MAGNETISM; SYMMETRY; SYSTEMS |
| 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: | 28 Feb 2023 10:13 |
| Last Modified: | 28 Feb 2023 10:13 |
| URI: | https://pred.uni-regensburg.de/id/eprint/50137 |
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