Uniform semiclassical trace formula for U(3) → SO(3) symmetry breaking

Brack, M.Institut für Theoretische Physik, Universität Regensburg, Regensburg, Germany (författare)

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 ωr:ωφ ≤ N:M of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential V(r) ∝ r4.

Ögren, Magnus,1977-Lund University,Lunds universitet,Matematisk fysik,Fysiska institutionen,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematical Physics,Department of Physics,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)matf-mog (författare)
Yu, YongleLund University,Lunds universitet,Matematisk fysik,Fysiska institutionen,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematical Physics,Department of Physics,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)matf-yly (författare)
Reimann, StephanieLund University,Lunds universitet,Matematisk fysik,Fysiska institutionen,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematical Physics,Department of Physics,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)matf-sre (författare)
Institut für Theoretische Physik, Universität Regensburg, Regensburg, GermanyMatematisk fysik (creator_code:org_t)

Ingår i:Journal of Physics A: Institute of Physics (IOP)38:46, s. 9941-99670305-44701361-6447

Av författaren/redakt...: Brack, M.; Ögren, Magnus, 1 ...; Yu, Yongle; Reimann, Stephan ...

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