Two-dimensional quantum spectra and classical orbits of isosceles- right triangular billiards

Liu Xiang-Long; Zhu Man-Zuo; Lu Lu

doi:10.7498/aps.61.220301

Abstract

The quantum spectra are derived from the wave-functions and the energy-functions of the isosceles-right triangular model. Although the eigenstates of the billiard system are not separable, the problem of functions with two variables is exactly solvable. The numerical results of the Fourier transform of quantum spectral functions are compared with the results from the classical orbits whose lengths match well with the positions of the spectra peaks. This result gives a new evident for the correspondence of quantum and classical mechanics.

Keywords:

Authors and contacts

1.
School of Electronic Engineering Xi’dian University, Xi’an 710071, China
Funds: Project supported by the Natual Science Foundation of Shaanxi Province, China.

References

[1]	Esaki L, Tus R 1970 IBMJ Res. Dev. 14 61
[2]	Gutzwiller MC 1990 Chaos in Classical and Quantum Mechanics (New York: Springer)
[3]	Liao Q H, Liu Z D, You S P, Cao C Q 2007 Acta Sinica Quantum Optica 13 304 (in Chinese) [廖庆洪, 刘正东, 尤素萍, 曹昌祺 2007 量子光学学报 13 304]
[4]	Huang G M, Liu Y M 2009 Journal of Atomic and Molecular Physics 26 447 (in Chinese) [黄钢明刘益民2009 原子与分子物理学报 26 447]
[5]	Zhang L Q, Zhang Y H, Xu X Y, Wang Y J, Lin S L, Du M L 2007 Journal of Atomic and Molecular Physics 24 69 (in Chinese) [张丽琴, 张延惠, 徐学友, 王雅静, 林圣路, 杜孟利 2007 原子与分子物理学报 24 69]
[6]	Zhu M Z, Wang Z X, Mei C 2011 Journal of Atomic and Molecular Physics (in press) (in Chinese) [朱满座, 王志霞, 梅超2011 原子与分子物理学报 (in press)]
[7]	Jun L 2008 Progress in Nature Science 18 927
[8]	Robinett R W 1998 Math. Phys. 39 278
[9]	Robinett R W 1997 Am. J. Phys. 65 1167
[10]	Lu J, Du M L 2004 Acta Phys. Sin. 53 2450 (in Chinese) [陆军, 杜孟丽 2004 物理学报 53 2450]
[11]	Lin S L, Gao F, Hong Z P, Du M L 2004 Chin. Phys. Lett. 22 9

Cited By

[1]	Esaki L, Tus R 1970 IBMJ Res. Dev. 14 61
[2]	Gutzwiller MC 1990 Chaos in Classical and Quantum Mechanics (New York: Springer)
[3]	Liao Q H, Liu Z D, You S P, Cao C Q 2007 Acta Sinica Quantum Optica 13 304 (in Chinese) [廖庆洪, 刘正东, 尤素萍, 曹昌祺 2007 量子光学学报 13 304]
[4]	Huang G M, Liu Y M 2009 Journal of Atomic and Molecular Physics 26 447 (in Chinese) [黄钢明刘益民2009 原子与分子物理学报 26 447]
[5]	Zhang L Q, Zhang Y H, Xu X Y, Wang Y J, Lin S L, Du M L 2007 Journal of Atomic and Molecular Physics 24 69 (in Chinese) [张丽琴, 张延惠, 徐学友, 王雅静, 林圣路, 杜孟利 2007 原子与分子物理学报 24 69]
[6]	Zhu M Z, Wang Z X, Mei C 2011 Journal of Atomic and Molecular Physics (in press) (in Chinese) [朱满座, 王志霞, 梅超2011 原子与分子物理学报 (in press)]
[7]	Jun L 2008 Progress in Nature Science 18 927
[8]	Robinett R W 1998 Math. Phys. 39 278
[9]	Robinett R W 1997 Am. J. Phys. 65 1167
[10]	Lu J, Du M L 2004 Acta Phys. Sin. 53 2450 (in Chinese) [陆军, 杜孟丽 2004 物理学报 53 2450]
[11]	Lin S L, Gao F, Hong Z P, Du M L 2004 Chin. Phys. Lett. 22 9

[1]	Qiang Jin, He Kai-Zhou, Liu Dong-Ni, Lu Qi-Hai, Han Gen-Liang, Song Yu-Zhe, Wang Xiang-Qian. Study of magnetic vortex spin wave mode in triangular structures. Acta Physica Sinica, 2022, 71(19): 194703. doi: 10.7498/aps.71.20221128
[2]	Liu Zhi-Xin, Dang Zhi-Bo, Fang Zhe-Yu. Electron beam chiral diffraction radiation in isosceles right triangle light-well. Acta Physica Sinica, 2022, 71(24): 247801. doi: 10.7498/aps.71.20221417
[3]	Meng Miao, Yan De-Xian, Li Jiu-Sheng, Sun Shuai. Research on negative curvature terahertz fiber based on nested triangle structure cladding. Acta Physica Sinica, 2020, 69(16): 167801. doi: 10.7498/aps.69.20200457
[4]	Dong Guo-Dan, Zhang Huan-Hao, Lin Zhen-Ya, Qin Jian-Hua, Chen Zhi-Hua, Guo Ze-Qing, Sha Sha. Numerical investigations of interactions between shock waves and triangular cylinders in magnetic field. Acta Physica Sinica, 2018, 67(20): 204701. doi: 10.7498/aps.67.20181127
[5]	Hu Rui, Fan Zhi-Qiang, Zhang Zhen-Hua. Magneto-electronic and magnetic transport properties of triangular graphene quantum-dot arrays. Acta Physica Sinica, 2017, 66(13): 138501. doi: 10.7498/aps.66.138501
[6]	Tian Zi-Jian, Li Wei-Xiang, Fan Jing. Performance analysis of double incidence derivative metamaterial based on double-triangular structure. Acta Physica Sinica, 2015, 64(3): 034102. doi: 10.7498/aps.64.034102
[7]	Xin Jun-Li, Shen Jun-Xia. Correspondences between quantum and classical orbits Berry phases and Hannay angles for harmonic oscillator system. Acta Physica Sinica, 2015, 64(24): 240302. doi: 10.7498/aps.64.240302
[8]	Liu Zhi-Gang, Liu Wei-Long, Zhao Hai-Jun. Quantum calculations for photodetachment cross sections of H- in an equilateral triangle cavity. Acta Physica Sinica, 2015, 64(16): 163202. doi: 10.7498/aps.64.163202
[9]	Li Jing, Ning Ti-Gang, Pei Li, Jian Wei, Zheng Jing-Jing, You Hai-Dong, Sun Jian, Wang Yi-Qun, Li Chao. Experimental demonstration on triangular-shaped pulse train generation based on harmonic fitting. Acta Physica Sinica, 2014, 63(15): 154210. doi: 10.7498/aps.63.154210
[10]	Zhang Zhi-Dong, Gao Si-Min, Wang Hui, Wang Hong-Yan. Resonance mode of an equilateral triangle with triangle notch. Acta Physica Sinica, 2014, 63(12): 127301. doi: 10.7498/aps.63.127301
[11]	Qin Chen-Chen, Yang Shuang-Bo. Quantum chaos for two-dimensional Sinai billiard. Acta Physica Sinica, 2014, 63(14): 140507. doi: 10.7498/aps.63.140507
[12]	Wang Hua. Experimental research of triangular optical pulse generation in normal dispersive fiber. Acta Physica Sinica, 2012, 61(12): 124212. doi: 10.7498/aps.61.124212
[13]	Wang Yu-Bo, Song Li-Jun, Yan Dong, Gai Yong-Jie. Relations of classical-quantum correspondencein Dicke model. Acta Physica Sinica, 2011, 60(2): 020302. doi: 10.7498/aps.60.020302
[14]	Li Jing, Ning Ti-Gang, Pei Li, Zhou Qian, Hu Xu-Dong, Qi Chun-Hui, Gao Song, Yang Long. Fabrication of triangular chirped fiber Bragg grating and its application in single-sideband modulation based radio over fiber system. Acta Physica Sinica, 2011, 60(5): 054203. doi: 10.7498/aps.60.054203
[15]	Shi Yong, Ma Shan-Jun. Yang Hui Triangle symmetry and higher-order differential equations of motion. Acta Physica Sinica, 2006, 55(10): 4991-4994. doi: 10.7498/aps.55.4991
[16]	Wu Qing-Song, Zhao Yan, Zhang Cai-Bei, Li Feng. Self-assembling behavior and optical properties of triangular silver nanoplates. Acta Physica Sinica, 2005, 54(3): 1452-1456. doi: 10.7498/aps.54.1452
[17]	Xu Xue-You, Zhang Yan-Hui, Huang Fa-Zhong, Lin Sheng-Lu, Du Meng-Li. Spectra analysis of the two-dimensional elliptic billiards. Acta Physica Sinica, 2005, 54(10): 4538-4542. doi: 10.7498/aps.54.4538
[18]	Lu Jun, Du Meng-Li. From quantum spectra to classical orbits: the rectangular billiards. Acta Physica Sinica, 2004, 53(8): 2450-2453. doi: 10.7498/aps.53.2450
[19]	CHEN HE-SHENG. THE QUANTUM TRANSPORT PROPERTIES OF A 1-DIMENSIONAL KICKED BILLIARDS MODEL. Acta Physica Sinica, 2000, 49(5): 844-848. doi: 10.7498/aps.49.844
[20]	Pan Li-zhou. NOTE ON THE INFLUENCE FUNCTION FOR THE DEFLECTION OF AN EQUILATERAL TRIANGULAR PLATE SIMPLY SUPPORTED AT THE EDGES. Acta Physica Sinica, 1956, 12(6): 632-642. doi: 10.7498/aps.12.632

Catalog

Vol. 61, Issue 22 - 2012-11-20

Metrics

Abstract views: 8743
PDF Downloads: 494
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板