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

  • 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.
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  • [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
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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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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

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.

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