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 |
| Publication status | Published - 2000 |
| Externally published | Yes |
Fingerprint
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
A functional equation for semiclassical Fredholm determinant for strongly chaotic billiards. / Harayama, Takahisa; Shudo, Akira; Tasaki, Shuichi.
In: Progress of Theoretical Physics Supplement, No. 139, 2000, p. 460-469.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A functional equation for semiclassical Fredholm determinant for strongly chaotic billiards
AU - Harayama, Takahisa
AU - Shudo, Akira
AU - Tasaki, Shuichi
PY - 2000
Y1 - 2000
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0034412267&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0034412267&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0034412267
SP - 460
EP - 469
JO - Progress of Theoretical Physics
JF - Progress of Theoretical Physics
SN - 0033-068X
IS - 139
ER -