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Uniform semiclassical trace formula for *U*(3) → *SO*(3) symmetry breakingPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 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]

##### Place, publisher, year, edition, pages

Institute of Physics (IOP), 2005. Vol. 38, no 46, p. 9941-9967
##### National Category

Other Physics Topics
##### Identifiers

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: diva2:1188780
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Available from: 2018-03-08 Created: 2018-03-08 Last updated: 2018-03-12Bibliographically approved

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 ω_{r}:ω_{φ} ≤ N:M of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential V(r) ∝ r^{4}.

doi
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