Brack, Matthias and Ögren, M. and Yu, Y. and Reimann, Stephanie (2005) Uniform semiclassical trace formula for U(3) --> SO(3) symmetry breaking. Journal of Physics A 38, pp. 9941-9967.
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 in semiclassical perturbation theory by integration of the action of the perturbed periodic HO orbit families over the manifold P which is covered by the parameters describing their four-fold degeneracy. Then we obtain an analytical uniform trace formula for arbitrary 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 (or energy) 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 by the orbits with the largest classical degeneracy, which are the three-fold degenerate tori with rational ratios of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential .
|Institutions:||Physics > Institute of Theroretical Physics > Chair Professor Schäfer > Group Matthias Brack|
|Projects:||Graduiertenkolleg Nichtlinearität und Nichtgleichgewicht|
|Subjects:||500 Science > 530 Physics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Yes|
|Deposited On:||20 Mar 2007|
|Last Modified:||20 Jul 2011 21:00|