Blaschke, J. and Brack, Matthias (1997) Periodic orbit theory of a circular billiard in homogeneous magnetic fields. PHYSICAL REVIEW A, 56 (1). pp. 182-194. ISSN 2469-9926, 2469-9934
Full text not available from this repository.Abstract
We present a semiclassical description of the level density of a two-dimensional circular quantum dot;in a homogeneous magnetic field. We model the total potential (including electron-electron interaction) of the dot containing many electrons by a circular billiard, i.e., a hard-wall potential. Using the extended approach df the Gutzwiller theory developed by Creagh and Littlejohn, we derive an analytic semiclassical trace formula. For its numerical evaluation we use a generalization of the common Gaussian smoothing technique. In strong fields orbit bifurcations, boundary effects (grazing orbits) and diffractive effect's (creeping orbits) come into play, and the comparison with the exact quantum-mechanical result shows major deviations. We show that the dominant corrections stem from grazing orbits, the other effects being much less important. We implement the boundary effects, replacing the Maslov index by a quantum-mechanical reflection/phase, and obtain a good agreement between the semiclassical and the quantum result for all field strengths, With this description, we are able to explain the main features of the gross-shell structure in terms of just one or two classical periodic orbits.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | METAL-CLUSTERS; SPECTRUM; QUANTIZATION; SUPERSHELLS; MECHANICS; EQUATION |
| 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: | 27 Apr 2023 06:14 |
| Last Modified: | 27 Apr 2023 06:14 |
| URI: | https://pred.uni-regensburg.de/id/eprint/50735 |
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