A CLASSICAL MODLE OF QUANTUM BERRY'S PHASE FACTOR

SUN Chang-Pu

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2024年10月30日

Chinese Physics C> 1989, Vol. 13> Issue(2) : 109-115

A CLASSICAL MODLE OF QUANTUM BERRY'S PHASE FACTOR

SUN Chang-Pu ^,

Northeast Normal University,Changchun

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Abstract：
Considering that the classical evolution equations are similar to the Schrodinger eqaution,we point out that there is the structure of the Berry's Phase in the solution of a classical evolution eqaution with adiabatic changing parameters.Thus,we can use a classical evolution process to imitate the quantum adiabatic process.As an example,the motion of a charged particle in slowly-changing magnetic field is studied and the corresponding phase factor can be interpreted as a holomony of the fiber bundle on the sphare s² in the parameter space.

References

[1]

M. V. Berry, Proc. R. Soc. Lend, A392(1954) . 45[2] B. Simon, Phys. Rev. Lett., 51(1983), 2167[3] R. Jackiw, MIT-CTPpieprint (1987).[4] P. Nelson and L. Alvez-Galm, Comm. Math. Phys., 39(1985),103[5] G. W. Semenoff and P. Sodana, Phys. Rev. Lett., 57(1980). 1195.[6] G. Delacreraz et al., Phys. Rev. Lett., 57(1985), 2598.[7] A. Toinita and R. Y. Chiao, Phys. Rev. Lett., 57 (1986) . 937[8] K. Tycko, Phys. Rev. Lett., 58(1987), 2281.[9] R. S. Nikam and P. Ring, Phys. Rev, Lett., 59(1987). 980.[10] Y .Aharonov and J. Anandan. Phys. Rev. Lett.. 53(1987), 1593.[11] 孙昌璞，高能物理与核物理,12(1987),351.Chang-pu Sun, J . Phys. A: Merh. Gen., 21(1983), in press.[12] J. Bitter and D. Dubber, Phys. Rev. Lett.,55(1987), 251.[13] M.V . Berry, J. Phys. A: Meth. Gen., 18(1985) . 15.J. H. Hannay, J. Phys. A:Meth. Gen., 18(1985), 221.[14] E. Gozzi and W. D. Thacker. Phys; Rev., D35(1987) 2388; 2398.[15] F. WILezek and A. Zee, Phys. Rev. Lett.. 52( 1884), 2111.

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SUN Chang-Pu. A CLASSICAL MODLE OF QUANTUM BERRY'S PHASE FACTOR[J]. Chinese Physics C, 1989, 13(2): 109-115.

SUN Chang-Pu. A CLASSICAL MODLE OF QUANTUM BERRY'S PHASE FACTOR[J]. Chinese Physics C, 1989, 13(2): 109-115. shu

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

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1.
沈阳化工大学材料科学与工程学院沈阳 110142

A CLASSICAL MODLE OF QUANTUM BERRY'S PHASE FACTOR

SUN Chang-Pu ^,

Corresponding author: SUN Chang-Pu,

Northeast Normal University,Changchun

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1989-02-05

Abstract: Considering that the classical evolution equations are similar to the Schrodinger eqaution,we point out that there is the structure of the Berry's Phase in the solution of a classical evolution eqaution with adiabatic changing parameters.Thus,we can use a classical evolution process to imitate the quantum adiabatic process.As an example,the motion of a charged particle in slowly-changing magnetic field is studied and the corresponding phase factor can be interpreted as a holomony of the fiber bundle on the sphare s² in the parameter space.