Classical Model for Quantum Berry's Phase Factors

Sun Changpu

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

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

Abstract
HTML
Reference
Related

PDF

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.

[1]	Mustapha Maamache , Jeong Ryeol Choi . Quantum-classical correspondence for the inverted oscillator. Chinese Physics C, 2017, 41(11): 113106. doi: 10.1088/1674-1137/41/11/113106
[2]	WU Qing , ZHOU Li-Juan , XIANG Qian-Fei , MA Wei-Xing . Multiquark cluster form factors in the relativistic harmonic oscillator model. Chinese Physics C, 2015, 39(1): 013102. doi: 10.1088/1674-1137/39/1/013102
[3]	LI Jian , SONG Dan-Jie , GUO Xiao-Jing , JING Bo . A quantum secure direct communication protocol based on a five-particle cluster state and classical XOR operation. Chinese Physics C, 2012, 36(1): 31-36. doi: 10.1088/1674-1137/36/1/005
[4]	LIU Wei-Wei , LUO Zhi-Quan , YANG Juan , BIAN Gang . Quantum tunnelling of higher-dimensional Kerr-anti-de Sitter black holes beyond semi-classical approximation. Chinese Physics C, 2011, 35(1): 22-25. doi: 10.1088/1674-1137/35/1/005
[5]	ZHU Jing-Min . Quantum phase transitions about parity breaking in matrix product systems. Chinese Physics C, 2011, 35(2): 144-148. doi: 10.1088/1674-1137/35/2/007
[6]	WEI Gao-Feng , LONG Chao-Yun , LONG Zheng-Wen , QIN Shui-Jie , FU Qiang . Classical mechanics in non-commutative phase space. Chinese Physics C, 2008, 32(5): 338-341. doi: 10.1088/1674-1137/32/5/002
[7]	ZHANG ZhongCan , FANG ZhenYun , HU ChenGuO , SUN ShiJun . Berry Geometric Phase and Quantum Transition. Chinese Physics C, 2000, 24(12): 1106-1114.
[8]	Zhang Zhongcan , Fang Zhenyun , Hu Chenguo , Sun Shijun . The Extention of Berry's Theory on Geometric Phase. Chinese Physics C, 1999, 23(10): 980-991.
[9]	Shen Yuelin , Ni Guangjiong . Berry's Connection and Wu-Yang's Monopole Potential. Chinese Physics C, 1995, 19(6): 500-507.
[10]	Meng Jie , Zeng Jinyan , Zhao Enguang . Berry Phase and Pair Transfer Matrix Element in Rotating Nuclei. Chinese Physics C, 1994, 18(3): 249-255.
[11]	SUN Chang-Pu , PAN Lin , GE Mo-Lin . Effective topological action in Heisenberg spin model as Berry's phase. Chinese Physics C, 1992, 16(3): 202-207.
[12]	Sun Changpu , Pang Lin , Ge Molin . Effective Topological Action in Heisenberg Spin Model as Berry's Phase. Chinese Physics C, 1992, 16(S1): 51-56.
[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.
[15]	SUN Chang-Pu , ZHANG Lin-Zhi . BERRY'S PHASE FACTORS IN MOVING FRAMES OF REFERENCE AND THEIR OBSERVABLE EFFECTS. Chinese Physics C, 1990, 14(2): 136-144.
[16]	Sun Changpu . Topological Action Related to Berry's Phase and its Non-adiabatic Effects. Chinese Physics C, 1990, 14(S3): 265-273.
[17]	Sun Changpu , Zhang Linzhi . Berry's Phase Factor in a Moving Reference Frame and Its Observable Effects in Physics. Chinese Physics C, 1990, 14(S1): 71-81.
[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.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1987-10-08

Article Metric

Article Views(473)
PDF Downloads(4)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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.