Classical Model for Quantum Berry's Phase Factors

Sun Changpu

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2024年10月30日

Chinese Physics C> 1989, Vol. 13> Issue(S1) : 15-22

Classical Model for Quantum Berry's Phase Factors

Sun Changpu

Department of Physics, Northeast Normal University, Changchun

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Abstract：
Having considered the similarity between the classical evolution equation and the Schrodinger equation, in this paper we show that a geometric phase factor with topological property,which we call the classical Berry's phase factor, appears properly in the solutions of the classical evolution equations with slowly-changing parameters. The general solutions of the approximate equations in any order in the non-degenerate case are given when the adiabatic condition is violated. As an example, an electrically charged particle moves in an adiabatically varying magnetic field is studied in detail, and a classical model for the Berry's phase factor is obtained explicitly. The phase factor can be explained in geometry as a holonomy of the hermitian linear fiber bundle on a unit sphere S² of the parameter space.

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[13]	SUN Chang-Pu . TOPOLOGICAL ACTION RELATIONG TO BERRY'S PHASE AND NON-ADIABATIC EFFECTS. Chinese Physics C, 1990, 14(8): 692-699.
[14]	GAO Xiao-Chun , XU Jing-Bo , QIAN Tie-Zheng , CHEN Cheng-Ming . THE MECHANICAL BERRY PHASE AND CORRESPONDING CLASSICAL TOPOLOGICAL PHASE ANGLE. Chinese Physics C, 1990, 14(8): 704-710.
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[18]	SUN Chang-Pu . A CLASSICAL MODLE OF QUANTUM BERRY'S PHASE FACTOR. Chinese Physics C, 1989, 13(2): 109-115.
[19]	SUN Chang-Pu . QUASI-ADIABATIC APPROXIMATION FOR THE SLOWLY-CHANGING QUANTUM PROCCESS AND BERRY PHASE FACTOR. Chinese Physics C, 1988, 12(3): 351-357.
[20]	Sun Changpu . Quasi-Adiabatic Approximation for Slowly-Changing Quantum System and Berry's Phase Factors. Chinese Physics C, 1988, 12(S3): 251-260.

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Sun Changpu. Classical Model for Quantum Berry's Phase Factors[J]. Chinese Physics C, 1989, 13(S1): 15-22.

Sun Changpu. Classical Model for Quantum Berry's Phase Factors[J]. Chinese Physics C, 1989, 13(S1): 15-22. shu

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Received: 1987-10-08

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沈阳化工大学材料科学与工程学院沈阳 110142

Classical Model for Quantum Berry's Phase Factors

Sun Changpu

Department of Physics, Northeast Normal University, Changchun

Received Date: 1987-10-08

Abstract: Having considered the similarity between the classical evolution equation and the Schrodinger equation, in this paper we show that a geometric phase factor with topological property,which we call the classical Berry's phase factor, appears properly in the solutions of the classical evolution equations with slowly-changing parameters. The general solutions of the approximate equations in any order in the non-degenerate case are given when the adiabatic condition is violated. As an example, an electrically charged particle moves in an adiabatically varying magnetic field is studied in detail, and a classical model for the Berry's phase factor is obtained explicitly. The phase factor can be explained in geometry as a holonomy of the hermitian linear fiber bundle on a unit sphere S² of the parameter space.