Classical Model for Quantum Berry's Phase Factors

Sun Changpu

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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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.