Magner, Alexander G. and Fedotkin, Sergey N. and Arita, Ken-ichiro and Misu, Toshiyuki and Matsuyanagi, Kenichi and Schachner, Thomas and Brack, Matthias (1999) Symmetry breaking and bifurcations in the periodic orbit theory. I - Elliptic billiard. PROGRESS OF THEORETICAL PHYSICS, 102 (3). pp. 551-598. ISSN 0033-068X,
Full text not available from this repository.Abstract
We derive an analytical trace formula for the level density of two-dimensional elliptic billiards using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all bifurcation points of the short diameter orbit and its repetitions, and possesses the correct limit of circular billiard at zero eccentricity. Away from the circular limit and the bifurcations, it reduces to the usual (extended) Gutzwiller trace formula, which for the leading-order families of periodic orbits is identical to the result of Berry and Tabor. We show that the circular disk limit of the diameter-orbit contribution is also reached through contributions from closed (periodic and non-periodic) orbits of the hyperbolic type with an even number of reflections from the boundary. We obtain the Maslov indices depending on deformation and energy in terms of the phases of the complex error and Airy functions. We find enhancement of the amplitudes near the common bifurcation points of short-diameter and hyperbolic orbits. The calculated semiclassical level densities and shell energies are in good agreement with the quantum mechanical ones.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SHELL STRUCTURE; SEMICLASSICAL INTERPRETATION; QUANTUM BILLIARD; DEFORMED-NUCLEI; BOUND SPECTRUM; OSCILLATOR; SYSTEMS; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Alumni or Retired Professors > Group Matthias Brack |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 11 Jan 2023 06:40 |
| Last Modified: | 11 Jan 2023 06:40 |
| URI: | https://pred.uni-regensburg.de/id/eprint/49058 |
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