Symmetry Reduction and Semiclassical Analysis of Axially Symmetric Systems

Details Symmetry Reduction and Semiclassical Analysis of Axially Symmetric Systems Symmetry Reduction and Semiclassical Analysis of Axially Symmetric Systems

1997-10-29

arxiv.org/abs/chao-dyn/9710023v1

Nonlinear Sciences

Chaotic Dynamics

23 pages (revtex) and a postscript file for figures; Phys. Rev. E (in press, scheduled for 01Jan98)

Scientific paper

10.1103/PhysRevE.57.1475

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 (\rho,z,p_\rho,p_z) and have p_\phi = 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_\phi varies smoothly.

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