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 fo...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 h→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.展开更多
基金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)+1 种基金the Provincial Foundation for Excellent Young Talents of Colleges and Universities of Anhui Province of China(Grant No.GXYQ2017014)the Anhui University Humanities and Social Sciences Research Project of China(Grant No.SK2019A0116).
文摘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 h→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.
