Quantum Classical Correspondence in a 2-Dimensional Deformed Harmonic Oscillator System

LIU Fang; LI Jun-Qing; XING Yong-Zhong

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2002, Vol. 26> Issue(9) : 949-954

Quantum Classical Correspondence in a 2-Dimensional Deformed Harmonic Oscillator System

Institute of Modern Physics, Northwest University, Xi'an 710069, China2 Institute of Modern Physics, The Chinese Academy of Sciences, Lanzhou 730000, China

Abstract
HTML
Reference
Related

PDF

Abstract：
The time evolution of expectation values of the basic dynamic variables in a quantum system under different effective Planck constant were compared with the exact values of the basic dynamic variables in classical system. It is found, for the regular motion, the difference comes from the quantum effect; for the chaotic motion, it comes from the dynamical effect and the destruction of the dynamical system. With these results, a correspondence between the quantum heterogeneity of the phase space and the Lyapunov exponent is made satisfactorily.

References

[1]

Gutzwiller M C. Chaos in Classical and Quantum Mechanics. Springer New York, 19902 GU Yan. Quantum Chaos, Shanghai Scientific and Technological Education Publishing House, Shanghai, 19963 XU Gong-Ou. Report in the 4th National Nuclear Reaction Conference, April, 19994 GU Yan. Physics Lett.，1990, A149(2,3):95-1005 Heirs W D et al. Phys. Rev. Lett.，1994, 72(15):2351-23546 LI Jun-Qing. J. Phys.，1998, 624:1021-10287 LIU Fang et al. High Energy Phys. and Nucl. Phys.，2000, 24(4):331-336 (in Chinese)(刘芳等.高能物理与核物理，2000,24(4):331-336)8 Wigner E P. Phys. Rev.，1932, 40 : 7499 Berry M V, Balazs N L. J. Phys.，1979, A12:625

[1]	WANG Peng , WANG Shun-Jin . Analytic Exact Solution of One-Dimentional Nonautonomous Classical Harmonic Oscillator. Chinese Physics C, 2005, 29(7): 651-656.
[2]	WANG Zhong-Qing , ZHOU Ping , ZHU Lian-Xuan , DAI Hong-Ying . Superposition of Generalized q-Coherent States of the Non-harmonicOscillator and Their Nonclassical Properties. Chinese Physics C, 2004, 28(4): 365-369.
[3]	LUO Xu-Dong , PENG Dan-Tao . Quantum Hall Fluid on Fuzzy Two Dimensional Sphere. Chinese Physics C, 2004, 28(10): 1040-1044.
[4]	YAN Jun , TAO Bi-You . A Electric Sine-Gordon Soliton Solution in Two-Dimensional Dilaton Gravity Model. Chinese Physics C, 2003, 27(9): 767-769.
[5]	WANG Zhong-Qing . Higher Power Squeezing Properties for Odd and Even Two-Parameter Deformed Coherent States. Chinese Physics C, 2001, 25(12): 1158-1164.
[6]	SONG Jian-Jun , LI Xi-Guo . Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System. Chinese Physics C, 2001, 25(10): 958-963.
[7]	Xu Ziwen . Q-Deformation of Generalized Coherent States in the Non-harmonic Oscillator Potential. Chinese Physics C, 1999, 23(5): 436-444.
[8]	Wang Jisuo , Sun Changyong , Teng Aiping . Quantum Statistic Properties of Eigenstates of the Annihilation Operatora_{qs^k of Two Parameter Deformed Harmonic Oscillator}. Chinese Physics C, 1997, 21(9): 793-800.
[9]	Wang Jisuo , Sun Changyong , He Jinyu . Eigenstates of the Higher Power of the Annihilation Operator ofTwo-Parameter Deformed Harmonic Oscillator. Chinese Physics C, 1996, 20(8): 703-706.
[10]	Zhou Huanqiang , Guan Xiwen , He Jingsong . A Two-Parameter Deformed Two-Dimensional Interacting Boson Model With U_qp(U₃)U_qp(U₂)U_qp(SO₂) Symmetry. Chinese Physics C, 1996, 20(1): 38-44.
[11]	Zhou Huanqiang , He Jingsong , Guan Xiwen . Some Remarks on a Two-Parameter Quantum Algebra SU_qs(2) and a Two-Parameter Deformed Harmonic Oscillator. Chinese Physics C, 1995, 19(5): 420-423.
[12]	Zhou Huanqiang , He Jingsong , Zhang Xinming . Eigenstates of the Second Power of the Annihilation Operator of Two-Parameter Deformed Harmonic Oscillator. Chinese Physics C, 1995, 19(3): 251-257.
[13]	YANG Xian-Jun , FAN Xi-Pei . State Densities of Deformed Nuclei Based on Axisymmetric Harmonic Oscillator Potential. Chinese Physics C, 1992, 16(5): 431-438.
[14]	WANG Zhong-Hua , WU Ke , GUO Han-Ying . The Cocycle Condition of Liouville Theory and Its Application to the 2-D Induced Gravity(Ⅱ). Chinese Physics C, 1991, 15(10): 881-889.
[15]	SU Gang , NIU Yun . THE CANONICAL TRANSFORMATION AND THE SPIN WAVE IN TWO DIMENSIONAL HEISENBERG ANTIFER-ROMAGNETIC SYSTEM. Chinese Physics C, 1990, 14(6): 500-503.
[16]	LI Wen-Zhu , YING He-Ping , DONG Shao-Jing . MONTE CARLO SIMULATION OF SU(2)×SU(2) SPIN SYSTEM ON 2-DIMENSIONAL RANDOM LATTICE. Chinese Physics C, 1987, 11(2): 186-191.
[17]	LIU MAO-SAN , WU WEN-TAI , LI SHU-SHEN , LIU YU-CHENG , SHI CAI-TU , ZHOU JIE-MIN . ANALYSIS OF TWO DIMENSIONAL FIELDS OF PERMANENT MAGNETIC MULTIPIECE LINEAR ARRAY SYSTEM. Chinese Physics C, 1982, 6(6): 764-767.
[18]	LIU MAO-SAN , WU WEN-TAI , LI SHU-ZHEN , LIU YU-CHENG , SHI CAI-TU , ZHOU JIE-MIN . PLANAR MULTIPOLE FIELD OF A PERMANENT MAGNET SYSTEM WITH QUASI-SEGMENTED AND TRAPEZOIDAL RING STRUCTURE. Chinese Physics C, 1982, 6(2): 251-254.
[19]	Liu Mao-san , Chen Ren-huai , Wu Wen-tai , Li Shu-zhen . PLANAR MULTIPOLE FIELD OF A PERMANENT MAGNET SYSTEM WITH MULTI-SEGMENTED RING STRUCTURE. Chinese Physics C, 1980, 4(6): 774-777.
[20]	HSXJ KUNG-NGOU . MASTER EQUATION FOR QUANTUM SYSTEMS. Chinese Physics C, 1978, 2(4): 359-367.

Access

Get Citation

LIU Fang, LI Jun-Qing and XING Yong-Zhong. Quantum Classical Correspondence in a 2-Dimensional Deformed Harmonic Oscillator System[J]. Chinese Physics C, 2002, 26(9): 949-954.

LIU Fang, LI Jun-Qing and XING Yong-Zhong. Quantum Classical Correspondence in a 2-Dimensional Deformed Harmonic Oscillator System[J]. Chinese Physics C, 2002, 26(9): 949-954. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2001-10-19
Revised: 1900-01-01

Article Metric

Article Views(4532)
PDF Downloads(523)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Quantum Classical Correspondence in a 2-Dimensional Deformed Harmonic Oscillator System

Corresponding author: LIU Fang,

Institute of Modern Physics, Northwest University, Xi'an 710069, China2 Institute of Modern Physics, The Chinese Academy of Sciences, Lanzhou 730000, China

Received Date: 2001-10-19
Accepted Date: 1900-01-01
Available Online: 2002-09-05

Abstract: The time evolution of expectation values of the basic dynamic variables in a quantum system under different effective Planck constant were compared with the exact values of the basic dynamic variables in classical system. It is found, for the regular motion, the difference comes from the quantum effect; for the chaotic motion, it comes from the dynamical effect and the destruction of the dynamical system. With these results, a correspondence between the quantum heterogeneity of the phase space and the Lyapunov exponent is made satisfactorily.