Symmetry Reduction and Semiclassical Analysis of Axially Symmetric Systems
arXiv:chao-dyn/9710023 · doi:10.1103/PhysRevE.57.1475
Abstract
We derive a semiclassical trace formula for a symmetry reduced part of the spectrum in axially symmetric systems. The classical orbits that contribute are closed in (ρ,z,p_ρ,p_z) and have p_ϕ= m\hbar where m is the azimuthal quantum number. For m > 0, these orbits vary with energy and almost never lie on periodic trajectories in the full phase space in contrast to the case of discrete symmetries. The transition from m=0 to m > 0 is however not dramatic as our numerical results indicate, suggesting that contributing orbits occur in topologically equivalent families within which p_ϕvaries smoothly.
23 pages (revtex) and a postscript file for figures; Phys. Rev. E (in press, scheduled for 01Jan98)