Semiclassical Fredholm determinant for strongly chaotic billiards

Takahisa Harayama, Akira Shudo, Shuichi Tasaki

研究成果: Article査読

9 被引用数 (Scopus)

抄録

We investigate the "semiclassical Fredholm determinant" for strongly chaotic billiards derived from the semiclassical limit of the Fredholm determinant of the boundary element method. We show that it is the same as a cycle-expanded Gutzwiller-Voros zeta function when the bounce number of the periodic orbit with the billiard boundary corresponds to the length of the symbolic sequence of its symbolic dynamical expression. A numerical experiment on a "concave triangle billiard" shows that the series defining the semiclassical Fredholm determinant does not converge absolutely in spite of the absolute convergence of the series defining the Fredholm determinant. However, the series behaves like an asymptotic series, and the finite sum obtained by optimal truncation of the series defining the semiclassical Fredholm determinant gives the semiclassical eigenenergies precisely enough such that the error of the semiclassical approximation is much smaller than the mean spacing of the exact eigenenergies.

本文言語English
ページ(範囲)1113-1149
ページ数37
ジャーナルNonlinearity
12
4
DOI
出版ステータスPublished - 1999 7 1
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学
  • 物理学および天文学(全般)
  • 応用数学

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