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

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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

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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

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

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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.

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Berry Geometric Phase and Quantum Transition

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