Calculation and Generalization of Non-Adiabatic Geometric Phase of Isotonic Oscillator with Operator Decomposition

An Nan; YANG Xin-E

Chinese Physics C> 2005, Vol. 29> Issue(4) : 350-353

Calculation and Generalization of Non-Adiabatic Geometric Phase of Isotonic Oscillator with Operator Decomposition

An Nan ^, ,
YANG Xin-E

Department of physics,School of Science,Tianjin University,Tianjin 300072,China

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Abstract：
Operator decomposition approach is used to calculate the non-adiabatic geometric phase of anharmonic oscillator. As an example we focus on isotonic oscillator, a type of anharmonic oscillator. The Aharonov-Anandan phase is derived when we choose base state and the first excitation state as cyclic initial states. Then we generalize our result by choosing three states or more states as cyclic initial states. Finally we give an general formula of Aharonov-Anandan phase for time-independent systems and discuss its applicability.

References

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. Berry M V. Proc. R. Soc. , 1984, A392: 45-572. Berry M V. J. Phys. A: Math. Gen. , 1985, 18: 15-273. Aharonov Y, Anandan J. Phys. Rev. Lett. , 1987, 20: 1593-15964. Moore D J. Phys. Rep. , 1991, 1: 1-435. Galogero F. J. Math. Phys. , 1969, 10: 2191-21966. Zhu D. J. Phys, 1987, A20: 4331-43367. XU Zi-Wen. Acta Physica Sinica, 1996, 45: 1807-1811 (in Chinese)(徐子二物理学报，1996,45:1807-1811)8. CHEN Chang-Yuan, LIU You-Wen. Acta Physica Sinica, 1998, 47:536-541 (in Chinese)(陈昌远，刘友文.物理学报，1998,47:536-541)

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An Nan and YANG Xin-E. Calculation and Generalization of Non-Adiabatic Geometric Phase of Isotonic Oscillator with Operator Decomposition[J]. Chinese Physics C, 2005, 29(4): 350-353.

An Nan and YANG Xin-E. Calculation and Generalization of Non-Adiabatic Geometric Phase of Isotonic Oscillator with Operator Decomposition[J]. Chinese Physics C, 2005, 29(4): 350-353. shu

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Received: 2004-07-12
Revised: 2004-08-07

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沈阳化工大学材料科学与工程学院沈阳 110142

Calculation and Generalization of Non-Adiabatic Geometric Phase of Isotonic Oscillator with Operator Decomposition

An Nan ^,
YANG Xin-E

Corresponding author: An Nan,

Department of physics,School of Science,Tianjin University,Tianjin 300072,China

Received Date: 2004-07-12
Accepted Date: 2004-08-07
Available Online: 2005-04-05

Abstract: Operator decomposition approach is used to calculate the non-adiabatic geometric phase of anharmonic oscillator. As an example we focus on isotonic oscillator, a type of anharmonic oscillator. The Aharonov-Anandan phase is derived when we choose base state and the first excitation state as cyclic initial states. Then we generalize our result by choosing three states or more states as cyclic initial states. Finally we give an general formula of Aharonov-Anandan phase for time-independent systems and discuss its applicability.