Abstract
We derive a functional equation for the Fredholm determinant of the boundary element method. By assuming that the functional equation holds for the semiclassical Fredholm determinant for strongly chaotic billiards, we obtain a real function whose zeros are the semiclassical eigenenergies. We also show by the numerical experiment of concave triangle billiards that the semiclassical eigenenergies are very close to the exact eigenenergies.
| Original language | English |
|---|---|
| Pages (from-to) | 460-469 |
| Number of pages | 10 |
| Journal | Progress of Theoretical Physics Supplement |
| Issue number | 139 |
| DOIs | |
| Publication status | Published - 2000 Jan 1 |
| Externally published | Yes |
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)
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Cite this
Harayama, T., Shudo, A., & Tasaki, S. (2000). A functional equation for semiclassical Fredholm determinant for strongly chaotic billiards. Progress of Theoretical Physics Supplement, (139), 460-469. https://doi.org/10.1143/PTPS.139.460