Semiclassical treatment of symmetry breaking and bifurcations in a non-integrable potential

We have derived an analytical trace formula for the level density of the Hénon-Heiles potential using the improved stationary phase method, based on extensions of Gutzwiller's semiclassical path integral approach. This trace formula has the correct limit to the standard Gutzwiller trace formula...

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Bibliographic Details
Published inPhysica scripta Vol. 90; no. 11; pp. 114011 - 114018
Main Authors Koliesnik, M V, Krivenko-Emetov, Ya D, Magner, A G, Arita, K, Brack, M
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.11.2015
Subjects
energy shell corrections
level density
periodic orbit theory
symmetry breaking
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Summary:We have derived an analytical trace formula for the level density of the Hénon-Heiles potential using the improved stationary phase method, based on extensions of Gutzwiller's semiclassical path integral approach. This trace formula has the correct limit to the standard Gutzwiller trace formula for the isolated periodic orbits far from all (critical) symmetry-breaking points. It continuously joins all critical points at which an enhancement of the semiclassical amplitudes occurs. We found a good agreement between the semiclassical and the quantum oscillating level densities for the gross shell structures and for the energy shell corrections, solving the symmetry breaking problem at small energies.
Bibliography:Royal Swedish Academy of Sciences
ISSN:0031-8949
1402-4896
DOI:10.1088/0031-8949/90/11/114011