Brack, Matthias and Ogren, M. and Yu, Y. and Reimann, S.M. (2005) Uniform semiclassical trace formula for U(3) -> SO(3) symmetry breaking. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 38 (46). pp. 9941-9967. ISSN 0305-4470,
Full text not available from this repository.Abstract
We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term 1/4 epsilon r(4). This term breaks the U(3) symmetry of the HO, resulting in a spherical system with SO(3) symmetry. We first treat the anharmonic term for small e in semiclassical perturbation theory by integration of the action of the perturbed periodic HO orbit families over the manifold CP2 which is covered by the parameters describing their four-fold degeneracy. Then, we obtain an analytical uniform trace formula for arbitrary E which in the limit of strong perturbations (or high energy) asymptotically goes over into the correct trace formula of the full anharmonic system with SO(3) symmetry, and in the limit E (or energy) -> 0 restores the HO trace formula with U(3) symmetry. We demonstrate that the gross-shell structure of this anharmonically perturbed system is dominated by the two-fold degenerate diameter and circular orbits, and not by the orbits with the largest classical degeneracy, which are the three-fold degenerate tori with rational ratios (omega(r) : omega(phi) = N : M of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential V(r) proportional to r(4).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PERIODIC-ORBITS; METAL-CLUSTERS; NONSEPARABLE SYSTEMS; INTEGRABLE SYSTEMS; BIFURCATIONS; QUANTIZATION; MECHANICS; APPROXIMATIONS; SUPERSHELLS; NANOWIRES; |
| 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: | 23 Apr 2021 06:58 |
| Last Modified: | 23 Apr 2021 06:58 |
| URI: | https://pred.uni-regensburg.de/id/eprint/35412 |
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