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

Abstract
HTML
Reference
Related

PDF

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

[1]

. 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)

[1]	XU Qiang , ZHU Sheng-Jiang . Splitting of Pseudospin and Spin Partners in the Relativistic Harmonic Oscillator. Chinese Physics C, 2007, 31(3): 251-257.
[2]	CHENG Yan-Fu , DAI Tong-Qing . Multiple-scale Perturbation Theory of Sextic Anharmonic Oscillator. Chinese Physics C, 2006, 30(6): 513-516.
[3]	WANG Peng , WANG Shun-Jin . Analytic Exact Solution of One-Dimentional Nonautonomous Classical Harmonic Oscillator. Chinese Physics C, 2005, 29(7): 651-656.
[4]	WANG Zhong-Qing , ZHOU Ping , ZHU Lian-Xuan , DAI Hong-Ying . Superposition of Generalized q-Coherent States of the Non-harmonicOscillator and Their Nonclassical Properties. Chinese Physics C, 2004, 28(4): 365-369.
[5]	WANG Ji-Suo , FENG Jian , LIU Tang-Kun , ZHAN Ming-Sheng . Antibunching Effect of Eigenstates of the Operator bQ－K in a Q-Deformed Non-harmonic Oscillator. Chinese Physics C, 2002, 26(6): 569-575.
[6]	WEI Shi , LIN Yu-Zheng . Accurate Computation on High Order Modes of Axial-symmetric Cavity with Vector Finite Element Method. Chinese Physics C, 2001, 25(10): 1017-1021.
[7]	WANG Zhong-Qing . Higher-Order Squeezing and Antibunching Effect for the Odd and Even Generalized q-Coherent States of the Non-harmonic Oscillator. Chinese Physics C, 2001, 25(11): 1044-1050.
[8]	WANG Zhong-Qing . Higher Power Squeezing Properties for Odd and Even Two-Parameter Deformed Coherent States. Chinese Physics C, 2001, 25(12): 1158-1164.
[9]	WANG Ji-Suo , LIU Tang-Kun , ZHAN Ming-Sheng . Higher-Order Squeezing for Generalized Odd and Even Coherent States of a Q-Deformed Non-harmonic Oscillator. Chinese Physics C, 2001, 25(1): 11-15.
[10]	WANG Zhong-Qing . Antibunching Effect for the Eigenstate of the Higher Powers of the Annihilation Operator of Two-Parameter Deformed Harmonic Oscillator. Chinese Physics C, 2001, 25(10): 964-970.
[11]	DUAN HuaiYu , LIU JuePing . Calculation of Anomalous Dimension of Three-Gluon Tensor Operators. Chinese Physics C, 2000, 24(7): 642-648.
[12]	WANG JiSuo , LIU TangKun , ZHAN MingSheng . Eigenstates of the Higher Powers of Annihilation Operator of a Q-Deformed Non-harmonic Oscillator and Their Higher-Order Squeezing. Chinese Physics C, 2000, 24(12): 1115-1122.
[13]	Zhang Zhongcan , Fang Zhenyun , Hu Chenguo , Sun Shijun . The Extention of Berry's Theory on Geometric Phase. Chinese Physics C, 1999, 23(10): 980-991.
[14]	Dong Yubing . Study on the Helicity Amplitudes of the Resonances Based on the Relativistic Harmonic Oscillator Model. Chinese Physics C, 1997, 21(11): 1035-1040.
[15]	YANG Xian-Jun , FAN Xi-Pei . State Densities of Deformed Nuclei Based on Axisymmetric Harmonic Oscillator Potential. Chinese Physics C, 1992, 16(5): 431-438.
[16]	DUAN Yi-Wu , WU Wei-Ping , BAO Cheng-Guang , AN Wei-Ke . The Expansion Method of Mixed Basis Vectors of Lower-energy States and Harmonic Oscillators in Calculation of Bound States of Few-Body Systems. Chinese Physics C, 1991, 15(1): 42-45.
[17]	CHEN Xue-Jun . EXPRESSIONS OF FERMION OPERATORS IN THE INTERACTING BOSON-FERMION MODELS. Chinese Physics C, 1990, 14(2): 160-163.
[18]	ZHOU Yuan-Hai , JIANG De-Sun , QIAN Wen-Jia , GONG Xue-Hui . THE HEAVY QUARKONIUM SPECTRUM OF ANHARMONIC OSCILLATORS CONFINEMENT POTENTIAL. Chinese Physics C, 1987, 11(2): 202-207.
[19]	TUAN I-SHIH , KEH MO-LIN . GEOMETRICAL DESCRIPTION OF DECOMPOSIBILITY OF A NON-ABELIAN GAUGE POTENTIAL. Chinese Physics C, 1978, 2(6): 511-514.
[20]	CHU CHUNG-YUAN AN ING , . A MODEL OF THE STRUCTURE OF MESONS WITH A COVARIANT OSCILLATOR POTENTIAL. Chinese Physics C, 1977, 1(1): 47-51.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Article Metric

Article Views(2930)
PDF Downloads(592)
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

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.