Open AccessDiffractive effect of quantum spectra in the annular billiard
Author(s) -
Zhang Ji-Quan,
Yanhui Zhang,
Zhou Hui,
Jia Zheng-Mao,
Shu Lin
Publication year - 2009
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.58.5965
Subject(s) - dynamical billiards , semiclassical physics , diffraction , physics , quantum , fresnel diffraction , spectrum (functional analysis) , spectral line , quantum mechanics , radius , orbit (dynamics) , classical mechanics , computer security , computer science , engineering , aerospace engineering
We analyze the quantum spectra of the two-dimensional annular billiard system based on the open-orbit quantum spectrum function, and respectively calculate the Fourier-transformed quantum spectra for various values of a parameter in the case f=Rin/Rout. The results show that the peak positions of quantum spectrum match with the lengths of classical orbits of particle motion very well and the semiclassical closed-orbit theory affords a good explanation. While the inner circle radius becomes comparaber with the de Brogile wavelength of the particle, the character of quantum spectrum changes essentially, turning out to be similar with the pattern of optical diffraction, which is a purely wavelike phenomenon and accords with Fresnel-Kirchhoff diffraction theorem. Our treatment provides a basis theory for researching the property of billiard system and microjunction transport, and opens a new way to investigate the diffraction of crystal and spectral analysis.