中国物理B ›› 2006, Vol. 15 ›› Issue (3): 502-506.doi: 10.1088/1009-1963/15/3/009

• GENERAL • 上一篇    下一篇

The quantum spectra analysis of the circular billiards in wells

张延惠1, 张丽琴1, 徐学友1, 葛美华1, 林圣路1, 杜孟利2   

  1. (1)College of Physics and Electronics, Shandong Normal University, Jinan 250014, China; (2)Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080, China
  • 收稿日期:2005-05-31 修回日期:2005-09-13 出版日期:2006-03-20 发布日期:2006-03-20
  • 基金资助:
    Project supported by the National Natural Foundation of China (Grant Nos 10374061 and 90403028).

The quantum spectra analysis of the circular billiards in wells

Zhang Yan-Hui (张延惠)a, Zhang Li-Qin (张丽琴)a, Xu Xue-You (徐学友)a, Ge Mei-Hua (葛美华)a, Lin Sheng-Lu (林圣路)a, Du Meng-Li (杜孟利)b   

  1. a College of Physics and Electronics, Shandong Normal University, Jinan 250014, China; b Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080, China
  • Received:2005-05-31 Revised:2005-09-13 Online:2006-03-20 Published:2006-03-20
  • Supported by:
    Project supported by the National Natural Foundation of China (Grant Nos 10374061 and 90403028).

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摘要： We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier-transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classical method provides a bridge between quantum and classical mechanics.

Abstract: We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier-transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classical method provides a bridge between quantum and classical mechanics.

Key words: circular billiard, closed-orbit theory, quantum spectra function, Fourier-transformed spectra

中图分类号:  (Semiclassical theories and applications)

  • 03.65.Sq