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Quantum-classical correspondence and mechanical analysis ofa classical-quantum chaotic system |
| Haiyun Bi(毕海云)1,3, Guoyuan Qi(齐国元)2, Jianbing Hu(胡建兵)1, Qiliang Wu(吴启亮)4 |
1 School of Mechanical Engineering, Tiangong University, Tianjin 300384, China;
2 Tianjin Key Laboratory of Advanced Technology of Electrical Engineering and Energy, Tiangong University, Tianjin 300384, China;
3 The Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education, and School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China;
4 Post-doctorate Research Station of Mechanical Engineering, School of Electrical Engineering and Automation, Tiangong University, Tianjin 300384, China |
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Abstract Quantum-classical correspondence is affirmed via performing Wigner function and a classical-quantum chaotic system containing random variables. The classical-quantum system is transformed into a Kolmogorov model for force and energy analysis. Combining different forces, the system is divided into two categories: conservative and non-conservative, revealing the mechanical characteristic of the classical-quantum system. The Casimir power, an analysis tool, is employed to find the key factors governing the orbital trajectory and the energy cycle of the system. Detailed analyses using the Casimir power and an energy transformation uncover the causes of the different dynamic behaviors, especially chaos. For the corresponding classical Hamiltonian system when Planck's constant ħ→0, the supremum bound of the system is derived analytically. Difference between the classical-quantum system and the classical Hamiltonian system is displayed through trajectories and energies. Quantum-classical correspondences are further demonstrated by comparing phase portrait, kinetic, potential and Casimir energies of the two systems.
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Received: 27 October 2019
Revised: 04 December 2019
Accepted manuscript online:
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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05.45.Mt
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(Quantum chaos; semiclassical methods)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61873186 and 11902220), the Natural Science Foundation of Tianjin City of China (Grant No. 17JCZDJC38300), the Provincial Foundation for Excellent Young Talents of Colleges and Universities of Anhui Province of China (Grant No. GXYQ2017014), and the Anhui University Humanities and Social Sciences Research Project of China (Grant No. SK2019A0116). |
Corresponding Authors:
Guoyuan Qi
E-mail: guoyuanqisa@qq.com
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Cite this article:
Haiyun Bi(毕海云), Guoyuan Qi(齐国元), Jianbing Hu(胡建兵), Qiliang Wu(吴启亮) Quantum-classical correspondence and mechanical analysis ofa classical-quantum chaotic system 2020 Chin. Phys. B 29 020502
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