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

SUN Chang-Pu

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

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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.

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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

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Received: 1900-01-01
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

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.