Chinese Physics C > 1988, Vol. 12 > Issue(3): 351-357

QUASI-ADIABATIC APPROXIMATION FOR THE SLOWLY-CHANGING QUANTUM PROCCESS AND BERRY PHASE FACTOR

SUN Chang-Pu^,

Northeast Normal University,Changchun

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Abstract：
By using group representation theory,the quasi-adiabatic approximation solution of the schrodinger equation of a quantum system with slowly-changing Hamiltonian are presented in this paper.We not only obtained the Berry phase factor and strictly proved the quantum adiabatic theorem as the zeroth-order approximation,but also studied the universal Berry phase factor and its geometrical interpretation when the adiabatic condition is violated.It is pointed out that this universal Berry phase factor has observable effects.

References

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Berry M. V. Proc. R. Soc. Lond, A 392(1984), 4 ; Simon B. Phys Rev. Lett., 54(1983), 2167.[2] Aharnnov Y and Bohm D Phys. Rev., 115(1959), 485.[3] Aharonov Y and Sussikind L Phys. Rev., 159(1957), 1237.[4] Delacretaz G et a1 Phys. Rev. Lett., 56(1986), 2598.[5] Chiao R Y and Wu Y S Phys. Rev. Lett., 57(1986), 933 Tomito A and Chiao R Y Phys. Rev. Lett., 57(1986), 937.[6] Nelson P and Alvarez-Gaume L Comm. Math. Phys., 99(1985), 103; Sonoda H Xucl. Bhyr, B266(1986),173; Niemi A J, Semenoff G W and Wu Y S Nucl. Phys., B266(1986), 410.[7] Semenoff G W and Sodano P Phys. Rev. Lett., 57(1986), 1159.Mead C A and Truhlar D G J. Chem. Phys., 70(1979), 2284.[8] Berry M V J. Phys. A: Mazh. Gen, 18(1985), 15; Hannay J H J. Phys. A: Mmh. Gen., 18(1985), 221;Gozzi E and Thacker W D 1987 MPI peprint MIP-PAE/PTH 67/86 .[9] Messiah A Quanzum Mechanics, Vol 2(1962), (North Holland: Amsterdam).

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SUN Chang-Pu. QUASI-ADIABATIC APPROXIMATION FOR THE SLOWLY-CHANGING QUANTUM PROCCESS AND BERRY PHASE FACTOR[J]. Chinese Physics C, 1988, 12(3): 351-357.

SUN Chang-Pu. QUASI-ADIABATIC APPROXIMATION FOR THE SLOWLY-CHANGING QUANTUM PROCCESS AND BERRY PHASE FACTOR[J]. Chinese Physics C, 1988, 12(3): 351-357. 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

QUASI-ADIABATIC APPROXIMATION FOR THE SLOWLY-CHANGING QUANTUM PROCCESS AND BERRY 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:1988-06-05

Abstract:By using group representation theory,the quasi-adiabatic approximation solution of the schrodinger equation of a quantum system with slowly-changing Hamiltonian are presented in this paper.We not only obtained the Berry phase factor and strictly proved the quantum adiabatic theorem as the zeroth-order approximation,but also studied the universal Berry phase factor and its geometrical interpretation when the adiabatic condition is violated.It is pointed out that this universal Berry phase factor has observable effects.