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 Lin Sheng-Lu |
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| Affiliation: | 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 spectralanalysis, this paper studies the correspondence between quantummechanics and the classical counterpart in a two-dimensional annularbilliard. The results demonstrate that the Fourier-transformedquantum spectra are in very good accordance with the lengths of the classicalballistic trajectories, whereas spectral strength isintimately associated with the shapes of possible open orbitsconnecting arbitrary two points in the annular cavity. This approachfacilitates an intuitive understanding of basic quantum featuressuch as quantum interference, locations of the wavefunctions, andallows 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 ofmicrojunction transport and even quantum chaos under the much moregeneral system. |
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| Keywords: | closed-orbit theory Fourier-transformed spectra annular billiard geometrical effect |
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