Development of quantum nonintegrability displayed in effective Hamiltonians: A three-level Lipkin model

Journal Article · Wed Mar 01 04:00:00 EST 1995 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.51.1770· OSTI ID:6437236

Gong-ou, Xu ^[1]; Jiang-bin, Gong ^[2]; Wen-ge, Wang ^[3]; Ya-tian, Yang ^[4]; De-ji, Fu ^[5]

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1. Department of Physics, Nanjing University, Nanjing 210008 (China) Department of Modern Physics, Lanzhou University, Lanzhou 730000 (China) National Laboratory of Heavy Ion Accelerator, Lanzhou 730000 (China) Institute of Nuclear Research, Shanghai, Academia Sinica, Shanghai 201800 (China)
2. Department of Physics, Nanjing University, Nanjing 210008 (China)
3. Institute of Nuclear Research, Shanghai, Academia Sinica, Shanghai 201800 (China)
4. Department of Physics, Fujian Normal University, Fuzhou 350007 (China)
5. China Center of Advanced Science and Technology (World Laboratory), Beijing (China) Institute of Nuclear Research, Shanghai, Academia Sinica, Shanghai 201800 (China)

The transition to chaos as the development of global nonintegrability in a three-level Lipkin model is investigated numerically. With effective Hamiltonians for different energy regions it is possible to study local statistical behaviors of the system in the corresponding energy regions. Behaviors of its classical counterparts are also given for comparison. The dynamical origin of statistical properties of effective Hamiltonian matrices is qualitatively explained. The question of what are the members of the Gaussian orthogonal ensemble is also discussed.

• OSTI ID: 6437236
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 51:3; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
661300 -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENSTATES
ENERGY SPECTRA
GAUSSIAN PROCESSES
HAMILTONIANS
MATHEMATICAL OPERATORS
MATRICES
QUANTIZATION
QUANTUM OPERATORS
SEMICLASSICAL APPROXIMATION
SPECTRA