・名古屋工業大学学術機関リポジトリは、名古屋工業大学内で生産された学術情報を電子的に収集・保存・発信するシステムです。 ・論文の著作権は、著者または出版社が保持しています。著作権法で定める権利制限規定を超える利用については、著作権者に許諾を得てください。 ・著者版フラグに「author」と記載された論文は、著者原稿となります。実際の出版社版とは、レイアウト、字句校正レベルの異同がある場合もあります。 ・Nagoya Institute of Technology Repository Sytem is built to collect, archive and offer electronically the academic information produced by Nagoya Institute of Technology. ・The copyright and related rights of the article are held by authors or publishers. The copyright owners' consents must be required to use it over the curtailment of copyrights. ・Textversion "Author " means the article is author's version. Author version may have some difference in layouts and wordings form publisher version.
We apply periodic orbit theory to a two-dimensional nonintegrable billiard system whose boundary is varied smoothly from a circular to an equilateral triangular shape. Although the classical dynamics becomes chaotic with increasing triangular deformation, it exhibits an astonishingly pronounced shell effect on its way through the shape transition. A semiclassical analysis reveals that this shell effect emerges from a codimension-2 bifurcation of the triangular periodic orbit. Gutzwiller’s semiclassical trace formula, using a global uniform approximation for the bifurcation of the triangular orbit and including the contributions of the other isolated orbits, describes very well the coarse-grained quantum-mechanical level density of this system.We also discuss the role of discrete symmetry for the large shell effect obtained here.
Anomalous shell effect in the transition from a circular to a triangular billiard
本文_fulltext
(952.42KB)
