### 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 |
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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 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Progress of Theoretical Physics Supplement*, (139), 460-469.

**A functional equation for semiclassical Fredholm determinant for strongly chaotic billiards.** / Harayama, Takahisa; Shudo, Akira; Tasaki, Shuichi.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics Supplement*, no. 139, pp. 460-469.

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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 -