SYMMETRY REDUCTION AND SEMICLASSICAL ANALYSIS OF AXIALLY-SYMMETRICAL SYSTEMS

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 (h ) over bar, where m is the azimuthal quantum number. For m not equal 0 , these orbits vary with energy and almost never lie on periodic traje ctories in the full phase space in contrast to the case of discrete sy mmetries. The transition from m = 0 to m > 0, however, is not as drama tic as our numerical results indicate, suggesting that contributing or bits occur in topologically equivalent families within which p(phi) va ries smoothly. [S1063-651X(98)02401-5].