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.
Received: 29 April 2008
Revised: 12 June 2008
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China (Grant Nos 10374061 and
10774093).
Cite this article:
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) The quantum spectral analysis of the two-dimensional annular billiard system 2009 Chin. Phys. B 18 35
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