Berry Geometric Phase and Quantum Transition

ZHANG ZhongCan; FANG ZhenYun; HU ChenGuO; SUN ShiJun

Chinese Physics C> 2000, Vol. 24> Issue(12) : 1106-1114

Berry Geometric Phase and Quantum Transition

Physics Department of Science College, ChongQing University, ChongQing 400044, China

Abstract
HTML
Reference
Related

PDF

Abstract：
For the emergence of Berry geometric phase, we analyze the relevant physical background condition of the weak transitions among quantum energy-levels. We elaborate a further discussion on the internal relationship between the strict obtainment of Berry geometric phase and the weak transitions. Our study shows that the strict obtainment of Berry geometric phase is the natural result of the adiabatic limit effect of weak transitions among quantum energy-levels. These transitions occur inevitably during the evolution process of quantum system.

References

[1]

Berry M V. Proc. Rog.Soc.Lond., 1984,A392: 45–57 2 Suter D, Mueller K T, Pines A. Phys. Rev. Lett., 1988, 60(13): 1218–1220; Tycko R. Phys. Rev. Lett., 1987, 58(22):2281–2284; Bitter T. Dubbers D. Phys. Rev. Lett., 1987, 59(3): 251–254; Richardson D J, Kilvington A I et al. Phys.Rev. Lett., 1988,61 (18): 2030–20333 Zygelman B. Phys. Rev. Lett., 1990, 64(3): 256–259; Mead C A. Phys. Rev. Lett., 1987, 59 (2); 161–164; Moody J,Shapere A, Wilczek F. Phys. Rev. Lett., 1986, 56(9): 893–896; Delacretaz G, Grant E R et al. Phys. Rev. Lett., 1986,56(24): 2598–26014 Chiao R Y, WU Y S. Phys. Rev. Lett., 1986, 57 (8):t 933–936; TOmita A, Chiao R Y. Phys. Rev. Lett., 1986, 57 (8):937–940; Simon R, Kimble H J, Sudarshan E C G. Phys. Rev. Lett., 1988, 61 (1): 19–22; Breuer H P, Dietz K,Holthaus M. Phys. Rev. 1993, A47 (1): 725–728 5 Zak J. Phys. Rev. 1989, B40(5): 3156–3161; Bird D M, Preston A R. Phys. Rev. Lett., 1988,61 (25): 2863–28666 LI H Z. Phys. Rev. Lett., 1987, 58(6): 539–542; Isler K, Paranjape M B. Phys. Rev., 1990, D41 (2): 561–563; NikamR S, Ring P. Phys. Rev. Lett., 1987, 58 (10): 980–983; Nikam R S, Ring P et al. Phys. Lett. 1990, B35 (3,4): 215–220; Liang J Q. Phys. Lett., 1989, A142(1): 11–137 ZHANG ZhongCan, FANG ZhengYun, HU ChenGuo et al. HEPNP(in Chinese), 1999, 23(10): 980–991(张忠灿,方祯云,胡陈果等.高能物理与核物理,1999,23(10):980–991)8 ZHANG ZhongCan, FANG ZhengYun, HU ChenGuo et al. Journal of Chongqing University(in Chinese), 1999, 22 (5):104–111(张忠灿,方祯云,胡陈果等.重庆大学学报,1999,22(5):104–111)9 NI G J,SUN P, KONG D. Journal of FuDan University(in Chinese), 1999,38(3):257–260(NI G J, SUN P, KONG D. 复旦学报, 1999,38(3):257–260)10 Aharonov Y,Anandan J. Phys. Rev. Lett., 1987,58(16): 1593–1596 11 NI G J,CHEN S Q,SHEN Y L. Phys. Lett., 1995, A197: 100–106 12 Berry M V. Proc. Rog. Soc. Lond., 1987, A414: 31–46 13 Berry M V. Proc. Rog. Soc. Lond., 1990, A430: 405–411

[1]	SONG Yuan-Jun , WANG Shun-Jin , ZHANG Guang-Biao . Nonadiabatic Geometric Phase and Hannay's Angle of the Nonautonomous Landau System in a Rotating Magnetic Field. Chinese Physics C, 2005, 29(7): 639-643.
[2]	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.
[3]	Shen Yuelin , Ni Guangjiong . Berry's Connection and Wu-Yang's Monopole Potential. Chinese Physics C, 1995, 19(6): 500-507.
[4]	Meng Jie , Zeng Jinyan , Zhao Enguang . Berry Phase and Pair Transfer Matrix Element in Rotating Nuclei. Chinese Physics C, 1994, 18(3): 249-255.
[5]	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.
[6]	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.
[7]	DING Yi-Bing , ZHOU Lei , QIN Dan-Hua , ZHAO Guang-Da . Dipole Sum Rules in Quantum Mechanics and Electric Depole Transitions of ψ(3770). Chinese Physics C, 1991, 15(12): 1076-1085.
[8]	QIN Dan-Hua , DING Yi-Bing , ZHAO Guang-Da . ON THE ELECTRIC DIPOLE TRANSITIONS OF ψ(3770). Chinese Physics C, 1990, 14(4): 380-384.
[9]	DING Lin-Kai . ON THE COLLISION GEOMETRY IN NUCLEAR INTERACTIONS. Chinese Physics C, 1990, 14(4): 303-310.
[10]	SUN Chang-Pu . TOPOLOGICAL ACTION RELATIONG TO BERRY'S PHASE AND NON-ADIABATIC EFFECTS. Chinese Physics C, 1990, 14(8): 692-699.
[11]	Sun Changpu . Topological Action Related to Berry's Phase and its Non-adiabatic Effects. Chinese Physics C, 1990, 14(S3): 265-273.
[12]	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.
[13]	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.
[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]	YU Yue , GUO Han-Ying . ON GEOMETRIC QUANTIZATION FOR BOSONIC STRING (Ⅱ). Chinese Physics C, 1989, 13(6): 503-511.
[16]	YU Yue , GUO Han-Ying . ON GEOMETRIC QUANTIZATION FOR THE BOSONIC STRINGS(1). Chinese Physics C, 1989, 13(5): 419-428.
[17]	Sun Changpu . Classical Model for Quantum Berry's Phase Factors. Chinese Physics C, 1989, 13(S1): 15-22.
[18]	SUN Chang-Pu . A CLASSICAL MODLE OF QUANTUM BERRY'S PHASE FACTOR. Chinese Physics C, 1989, 13(2): 109-115.
[19]	Sun Changpu . Quasi-Adiabatic Approximation for Slowly-Changing Quantum System and Berry's Phase Factors. Chinese Physics C, 1988, 12(S3): 251-260.
[20]	SUN Chang-Pu . QUASI-ADIABATIC APPROXIMATION FOR THE SLOWLY-CHANGING QUANTUM PROCCESS AND BERRY PHASE FACTOR. Chinese Physics C, 1988, 12(3): 351-357.

Access

Get Citation

ZHANG ZhongCan, FANG ZhenYun, HU ChenGuO and SUN ShiJun. Berry Geometric Phase and Quantum Transition[J]. Chinese Physics C, 2000, 24(12): 1106-1114.

ZHANG ZhongCan, FANG ZhenYun, HU ChenGuO and SUN ShiJun. Berry Geometric Phase and Quantum Transition[J]. Chinese Physics C, 2000, 24(12): 1106-1114. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1999-10-08
Revised: 1900-01-01

Article Metric

Article Views(3104)
PDF Downloads(549)
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

Berry Geometric Phase and Quantum Transition

Corresponding author: ZHANG ZhongCan,

Physics Department of Science College, ChongQing University, ChongQing 400044, China

Received Date: 1999-10-08

Accepted Date: 1900-01-01

Available Online: 2000-12-05

Abstract: For the emergence of Berry geometric phase, we analyze the relevant physical background condition of the weak transitions among quantum energy-levels. We elaborate a further discussion on the internal relationship between the strict obtainment of Berry geometric phase and the weak transitions. Our study shows that the strict obtainment of Berry geometric phase is the natural result of the adiabatic limit effect of weak transitions among quantum energy-levels. These transitions occur inevitably during the evolution process of quantum system.

HTML

Reference (1)

Berry Geometric Phase and Quantum Transition

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article