Open AccessSymmetry Breaking and Bifurcations in the Periodic Orbit Theory. II: Spheroidal Cavity
Author(s) -
A. G. Magner,
Ken-ichiro Arita,
S. N. Fedotkin,
K. Matsuyanagi
Publication year - 2002
Publication title -
progress of theoretical physics
Language(s) - English
Resource type - Journals
eISSN - 1347-4081
pISSN - 0033-068X
DOI - 10.1143/ptp.108.853
Subject(s) - physics , semiclassical physics , classification of discontinuities , plane (geometry) , bifurcation , symmetry (geometry) , orbit (dynamics) , classical mechanics , shell (structure) , planar , trace (psycholinguistics) , limit (mathematics) , quantum , symmetry breaking , action (physics) , quantum mechanics , quantum electrodynamics , mathematical analysis , geometry , nonlinear system , linguistics , philosophy , mathematics , materials science , computer graphics (images) , computer science , engineering , composite material , aerospace engineering
We derive a semiclassical trace formula for the level density of thethree-dimensional spheroidal cavity. To overcome the divergences anddiscontinuities occurring at bifurcation points and in the spherical limit, thetrace integrals over the action-angle variables are performed using an improvedstationary phase method. The resulting semiclassical level density oscillationsand shell energies are in good agreement with quantum-mechanical results. Wefind that the births of three-dimensional orbits through the bifurcations ofplanar orbits in the equatorial plane lead to considerable enhancement of shelleffect for superdeformed shapes.Comment: 49 pages, 18 figures, using PTPTeX.cls(included), submitted to Prog. Theor. Phy
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