The quantum spectral analysis of the two-dimensional annular billiard system |
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Authors: | Zhang Yan-Hui Zhang Ji-Quan Xu Xue-You and Lin Sheng-Lu |
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Institution: | College of Physics and Electronics, Shandong Normal University, Jinan 250014, China |
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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. |
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Keywords: | closed-orbit theory Fourier-transformed spectra annular billiard geometrical effect |
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