中国物理B ›› 2009, Vol. 18 ›› Issue (1): 35-39.doi: 10.1088/1674-1056/18/1/006

• GENERAL • 上一篇    下一篇

The quantum spectral analysis of the two-dimensional annular billiard system

张延惠, 张记全, 徐学友, 林圣路   

  1. College of Physics and Electronics, Shandong Normal University, Jinan 250014, China
  • 收稿日期:2008-04-29 修回日期:2008-06-12 出版日期:2009-01-20 发布日期:2009-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10374061 and 10774093).

The quantum spectral analysis of the two-dimensional annular billiard system

Zhang Yan-Hui(张延惠)†, Zhang Ji-Quan(张记全), Xu Xue-You(徐学友), and Lin Sheng-Lu(林圣路)   

  1. College of Physics and Electronics, Shandong Normal University, Jinan 250014, China
  • Received:2008-04-29 Revised:2008-06-12 Online:2009-01-20 Published:2009-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10374061 and 10774093).

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摘要： Based on the extended closed-orbit theory together with spectral analysis, this paper studies the correspondence between quantum mechanics and the classical counterpart in a two-dimensional annular billiard. The results demonstrate that the Fourier-transformed quantum spectra are in very good accordance with the lengths of the classical ballistic trajectories, whereas spectral strength is intimately associated with the shapes of possible open orbits connecting arbitrary two points in the annular cavity. This approach facilitates an intuitive understanding of basic quantum features such as quantum interference, locations of the wavefunctions, and allows quantitative calculations in the range of high energies, where full quantum calculations may become impractical in general. This treatment provides a thread to explore the properties of microjunction transport and even quantum chaos under the much more general system.

Abstract: Based on the extended closed-orbit theory together with spectral analysis, this paper studies the correspondence between quantum mechanics and the classical counterpart in a two-dimensional annular billiard. The results demonstrate that the Fourier-transformed quantum spectra are in very good accordance with the lengths of the classical ballistic trajectories, whereas spectral strength is intimately associated with the shapes of possible open orbits connecting arbitrary two points in the annular cavity. This approach facilitates an intuitive understanding of basic quantum features such as quantum interference, locations of the wavefunctions, and allows quantitative calculations in the range of high energies, where full quantum calculations may become impractical in general. This treatment provides a thread to explore the properties of microjunction transport and even quantum chaos under the much more general system.

Key words: closed-orbit theory, Fourier-transformed spectra, annular billiard, geometrical effect

中图分类号:  (Quantum chaos; semiclassical methods)

  • 05.45.Mt
03.65.Ge (Solutions of wave equations: bound states)