The quantum spectra analysis of the circular billiards in wells

doi:10.1088/1009-1963/15/3/009

Abstract

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.

Keywords: circular billiard closed-orbit theory quantum spectra function Fourier-transformed spectra

Received: 31 May 2005
Revised: 13 September 2005
Accepted manuscript online:

PACS:

03.65.Sq

(Semiclassical theories and applications)

Fund: Project supported by the National Natural Foundation of China (Grant Nos 10374061 and 90403028).

Cite this article:

Zhang Yan-Hui (张延惠), Zhang Li-Qin (张丽琴), Xu Xue-You (徐学友), Ge Mei-Hua (葛美华), Lin Sheng-Lu (林圣路), Du Meng-Li (杜孟利) The quantum spectra analysis of the circular billiards in wells 2006 Chinese Physics 15 502

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