Quasi-Adiabatic Approximation for Slowly-Changing Quantum System and Berry's Phase Factors

Sun Changpu

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2024年10月30日

Chinese Physics C> 1988, Vol. 12> Issue(S3) : 251-260

Quasi-Adiabatic Approximation for Slowly-Changing Quantum System and Berry's Phase Factors

Sun Changpu

Northeast Normal University, Changchun

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Abstract：
By analyzing the symmetry of a quantum system in terms of the method of the group theory, a quasi-adiabatic approximate method for solving a Schrodinger equation is presented. The method is to study the transition problem of the quantum system with the Hamiltonian that changes slowly but finitely. As a result of zeroth-order approximate, the quantum adiabatic theorem for the degenerate case is proved strictly, and the topological Berry's phase factors are introduced. A geometrical interpretation of the violation in the adiabatic condition is given, and it is demonstrated that the Berry^ phase factors exist generally in the quantum processes with the time scale which is comparable with the pericxJ of the Hamiltonian. Finally, a possible observable effect is pointed out of the Berry's phase factor in a slowly changing process where the adiabatic condition is violated.

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Sun Changpu. Quasi-Adiabatic Approximation for Slowly-Changing Quantum System and Berry's Phase Factors[J]. Chinese Physics C, 1988, 12(S3): 251-260.

Sun Changpu. Quasi-Adiabatic Approximation for Slowly-Changing Quantum System and Berry's Phase Factors[J]. Chinese Physics C, 1988, 12(S3): 251-260. shu

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Received: 1987-04-11

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沈阳化工大学材料科学与工程学院沈阳 110142

Quasi-Adiabatic Approximation for Slowly-Changing Quantum System and Berry's Phase Factors

Sun Changpu

Northeast Normal University, Changchun

Received Date: 1987-04-11

Abstract: By analyzing the symmetry of a quantum system in terms of the method of the group theory, a quasi-adiabatic approximate method for solving a Schrodinger equation is presented. The method is to study the transition problem of the quantum system with the Hamiltonian that changes slowly but finitely. As a result of zeroth-order approximate, the quantum adiabatic theorem for the degenerate case is proved strictly, and the topological Berry's phase factors are introduced. A geometrical interpretation of the violation in the adiabatic condition is given, and it is demonstrated that the Berry^ phase factors exist generally in the quantum processes with the time scale which is comparable with the pericxJ of the Hamiltonian. Finally, a possible observable effect is pointed out of the Berry's phase factor in a slowly changing process where the adiabatic condition is violated.