Quantum-classical correspondence and mechanical analysis ofa classical-quantum chaotic system

doi:10.1088/1674-1056/ab6205

中国物理B ›› 2020, Vol. 29 ›› Issue (2): 20502-020502.doi: 10.1088/1674-1056/ab6205

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Quantum-classical correspondence and mechanical analysis ofa classical-quantum chaotic system

Haiyun Bi(毕海云), Guoyuan Qi(齐国元), Jianbing Hu(胡建兵), Qiliang Wu(吴启亮)

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

收稿日期:2019-10-27 修回日期:2019-12-04 出版日期:2020-02-05 发布日期:2020-02-05
通讯作者: Guoyuan Qi E-mail:guoyuanqisa@qq.com
基金资助:
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).

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

Received:2019-10-27 Revised:2019-12-04 Online:2020-02-05 Published:2020-02-05
Contact: Guoyuan Qi E-mail:guoyuanqisa@qq.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: quantum, Wigner function, Hamiltonian system, force and energy transformation

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.

Key words: quantum, Wigner function, Hamiltonian system, force and energy transformation

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Mt (Quantum chaos; semiclassical methods)

毕海云, 齐国元, 胡建兵, 吴启亮. Quantum-classical correspondence and mechanical analysis ofa classical-quantum chaotic system[J]. 中国物理B, 2020, 29(2): 20502-020502.

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[J]. Chin. Phys. B, 2020, 29(2): 20502-020502.

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Quantum-classical correspondence and mechanical analysis ofa classical-quantum chaotic system

Quantum-classical correspondence and mechanical analysis ofa classical-quantum chaotic system

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