Uniform semiclassical trace formula for U(3) > SO(3) symmetry breaking
(2005) In Journal of Physics A: Mathematical and General19750101+01:0020070101+01:00 38(46). p.99419967 Abstract
 We develop a uniform semiclassical trace formula for the density of states of a threedimensional 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 fourfold 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)... (More)
 We develop a uniform semiclassical trace formula for the density of states of a threedimensional 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 fourfold 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 grossshell structure of this anharmonically perturbed system is dominated by the twofold degenerate diameter and circular orbits, and not by the orbits with the largest classical degeneracy, which are the threefold 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). (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/211535
 author
 Brack, M; Ögren, Magnus ^{LU} ; Yu, Yongle ^{LU} and Reimann, Stephanie ^{LU}
 organization
 publishing date
 2005
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Journal of Physics A: Mathematical and General19750101+01:0020070101+01:00
 volume
 38
 issue
 46
 pages
 9941  9967
 publisher
 IOP Publishing
 external identifiers

 wos:000233696200007
 scopus:27844470155
 ISSN
 03054470
 DOI
 10.1088/03054470/38/46/004
 language
 English
 LU publication?
 yes
 id
 ab72fd2b0f9c484b9f53607b7684599d (old id 211535)
 date added to LUP
 20070921 09:16:10
 date last changed
 20180107 08:35:19
@article{ab72fd2b0f9c484b9f53607b7684599d, abstract = {We develop a uniform semiclassical trace formula for the density of states of a threedimensional 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 fourfold 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 grossshell structure of this anharmonically perturbed system is dominated by the twofold degenerate diameter and circular orbits, and not by the orbits with the largest classical degeneracy, which are the threefold 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).}, author = {Brack, M and Ögren, Magnus and Yu, Yongle and Reimann, Stephanie}, issn = {03054470}, language = {eng}, number = {46}, pages = {99419967}, publisher = {IOP Publishing}, series = {Journal of Physics A: Mathematical and General19750101+01:0020070101+01:00}, title = {Uniform semiclassical trace formula for U(3) > SO(3) symmetry breaking}, url = {http://dx.doi.org/10.1088/03054470/38/46/004}, volume = {38}, year = {2005}, }