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Uniform semiclassical trace formula for U(3) → SO(3) symmetry breaking
Institut für Theoretische Physik, Universität Regensburg, Regensburg, Germany.
Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.ORCID iD: 0000-0002-2630-7479
Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
2005 (English)In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, no 46, p. 9941-9967Article in journal (Refereed) Published
Abstract [en]

We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term . 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 ε in semiclassical perturbation theory by integration of the action of the perturbed periodic HO orbit families over the manifold which is covered by the parameters describing their four-fold degeneracy. Then, we obtain an analytical uniform trace formula for arbitrary ε 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 ε (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 ωrφ ≤ N:M of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential V(r) ∝ r4.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2005. Vol. 38, no 46, p. 9941-9967
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URN: urn:nbn:se:oru:diva-65578DOI: 10.1088/0305-4470/38/46/004ISI: 000233696200007Scopus ID: 2-s2.0-27844470155OAI: oai:DiVA.org:oru-65578DiVA, id: diva2:1188780
Available from: 2018-03-08 Created: 2018-03-08 Last updated: 2018-03-12Bibliographically approved

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