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

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

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《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

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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

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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

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

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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.