Chinese Physics C > 1990, Vol. 14 > Issue(7): 604-613

HIGH-ORDER ADIABATIC APPROXIMATIONS FOR EVOLUTION OF DEGENERATE QUANTUM MECHANICAL SYSTEM AND NON-ABELIAN INDUCED GAUGE STRUCTURE

SUN Chang-Pu^,

Northeast Normal University,Changchun

Abstract
HTML
Reference
Related

PDF

Abstract：
In this paper high-order adiabatic approximate method is proposed to study the evolution of degenerate quantum systums with slowly-changing parameters and varying symmetry.We ont only prove the quantum adiabatic theorem for degenerate cases and discuss the corresponding non-abelian induced gauge structure,but also point out the non-adiabatic corrections resulting from higher-order approximations.With nuclear quadrupole resonance as an explicit example,we use this method to analyse observable effects of non-abelian Berry's phases in adiabatic and non-adiabatic experimental process.

References

[1]

M. V. Berry, Proc. R. Soc. Lond.; A392(1984), 45.R. Jackiw, Com. Atom. Mole, Phys.; 21(1988), 71, and therein.[2] R. Tycko, Phys. Rev, Lett., 58(1987), 2281.D. J. Richardson et. al. Phys. Pev, Lett., 61(1988),2030.[3] M. V. Betty, Proc. R. Soc. Lond., A414(1987), 47[4] N. Nakagawa, Ann. Phys., 179(1987), 145.[5] C.P. Sun, Chinese Phys. Lett., 6(1989), 97.[6] N. Papanicolaou. J. Phys. France, 49(1988), 1493.[7] C.P. Sun, J. Phys. A21(1988), 1595.[8] 孙昌璞，高能物理与核物理，12(1988)，352.

[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]	Medina Ablikim,HUANG Wei-Cheng,. New Realization of N=2 Supersymmetric QuantumMechanics and Shape Invariance. Chinese Physics C, 2002, 26(4): 338-345.
[3]	ZHANG De-Xing,CAI Shao-Hong. Quantum Mechanical Model with Nonlocal Potential. Chinese Physics C, 2002, 26(9): 895-899.
[4]	Wang Jiahui. Phase Structure of Z₃Lattice Gauge Theory Coupled With the Higgs Field. Chinese Physics C, 1999, 23(4): 352-359.
[5]	Huang Weicheng,Ruan Dong. N=4 Supersymmetric Quantum Mechanics. Chinese Physics C, 1995, 19(9): 812-819.
[6]	LI Fu-Bin. Construction of the Creation-Annihilation Operators for the Hydrogen Atom and Related Potentials with the Concepts of Supersymmetric Quantum Mechanics. Chinese Physics C, 1992, 16(6): 505-509.
[7]	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.
[8]	BIAN Jian-Guo. Non-Perturbative Propagators in QCD. Chinese Physics C, 1991, 15(11): 973-980.
[9]	QIU Rong. Constraint on the Parameter of Group By Two Order Transformation of Field Variable Being Equal to Zero in Non-Abelian. Chinese Physics C, 1991, 15(2): 111-116.
[10]	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.
[11]	QIU Rong. THE EQUIVALENCE OF TWO TRANSFORMATIONS OF THE INVARIANCE OF LAGRANGIAN FUNCTION IN NON-ABELIAN GAUGE FIELD. Chinese Physics C, 1989, 13(4): 302-308.
[12]	JING Si-Cong,RUAN Tu-Nan. ON THE QUANTIZATION OF PURE GAUGE FIELDS ON COSET SPACE OF ABELIAN CHIRAL GROUP. Chinese Physics C, 1988, 12(6): 773-781.
[13]	BAO Cheng-Guang,. SOLVING THE QUANTUM MECHANIC 5-BODY PROBLEMS. Chinese Physics C, 1988, 12(2): 273-276.
[14]	SUN Chang-Pu. QUASI-ADIABATIC APPROXIMATION FOR THE SLOWLY-CHANGING QUANTUM PROCCESS AND BERRY PHASE FACTOR. Chinese Physics C, 1988, 12(3): 351-357.
[15]	RUAN Tu-Nan,LIU Zu-Wei,JING Si-Cong. CONFINEMENT PROPERTIES OF THE PURE GAUGE FIELDS ON COSET SPACE OF A NON-ABELIAN CHIRAL GROUP. Chinese Physics C, 1984, 8(2): 158-166.
[16]	Dai Xian-xi,Huang Fa-yang,Ni Guang-jiong. THE BOUND STATE ENERGY LEVELS OF MONOPOLE PAIR AND OF CHARGED MONOPOLE-ELECTRON SYSTEM—SOME SINGULAR STATE PROBLEMS IN RELATIVISTIC QUANTUM MECHANICS. Chinese Physics C, 1980, 4(3): 313-321.
[17]	Ni Guang-jiong. THE LEVINSON THEOREM AND ITS GENERALIZATION IN RELATIVISTIC QUANTUM MECHANICS. Chinese Physics C, 1979, 3(4): 432-449.
[18]	Lee Hua-chung,Kuo Shuo-hung,Hsien Ting-chang. ON THE PROBLEM OF THE DUAL CHARGE (MAGNETIC MONOPOLE) OF NON-ABELLAN GROUPS (Ⅱ). Chinese Physics C, 1978, 2(1): 23-34.
[19]	DAI XIAN-XI,NI GUAN-JIONG. ON THE ELIMINATION OF PHASE ANGLE UNCERTAINTY IN SOME PROBLEMS OF RELATIVISTIC QUANTUM MECHANICS. Chinese Physics C, 1978, 2(3): 225-235.
[20]	TUAN I-SHIH,KEH MO-LIN. GEOMETRICAL DESCRIPTION OF DECOMPOSIBILITY OF A NON-ABELIAN GAUGE POTENTIAL. Chinese Physics C, 1978, 2(6): 511-514.

Access

Get Citation

SUN Chang-Pu. HIGH-ORDER ADIABATIC APPROXIMATIONS FOR EVOLUTION OF DEGENERATE QUANTUM MECHANICAL SYSTEM AND NON-ABELIAN INDUCED GAUGE STRUCTURE[J]. Chinese Physics C, 1990, 14(7): 604-613.

SUN Chang-Pu. HIGH-ORDER ADIABATIC APPROXIMATIONS FOR EVOLUTION OF DEGENERATE QUANTUM MECHANICAL SYSTEM AND NON-ABELIAN INDUCED GAUGE STRUCTURE[J]. Chinese Physics C, 1990, 14(7): 604-613. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1900-01-01
Revised: 1900-01-01

Article Metric

Article Views(4699)
PDF Downloads(428)
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

HIGH-ORDER ADIABATIC APPROXIMATIONS FOR EVOLUTION OF DEGENERATE QUANTUM MECHANICAL SYSTEM AND NON-ABELIAN INDUCED GAUGE STRUCTURE

SUN Chang-Pu^,

Corresponding author:SUN Chang-Pu,

Northeast Normal University,Changchun

Received Date:1900-01-01
Accepted Date:1900-01-01
Available Online:1990-07-05

Abstract:In this paper high-order adiabatic approximate method is proposed to study the evolution of degenerate quantum systums with slowly-changing parameters and varying symmetry.We ont only prove the quantum adiabatic theorem for degenerate cases and discuss the corresponding non-abelian induced gauge structure,but also point out the non-adiabatic corrections resulting from higher-order approximations.With nuclear quadrupole resonance as an explicit example,we use this method to analyse observable effects of non-abelian Berry's phases in adiabatic and non-adiabatic experimental process.