Quantization of the Periodic Orbits and Long-Range Correlations in Quantum Spectra

LI Xi-Guo; SONG Jian-Jun; XING Yong-Zhong; ZUO Wei

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2002, Vol. 26> Issue(5) : 484-490

Quantization of the Periodic Orbits and Long-Range Correlations in Quantum Spectra

Research Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Collisions, Lanzhou 730000, China2 Institute of Modern Physics, The Chinese Academy of Sciences, Lanzhou 730000, China

Abstract
HTML
Reference
Related

PDF

Abstract：
Using the classical quantization way in a two-dimensional integrable system and quantized energies-periodic orbits correspondence relationship, the long-range correlation among the quantum lavels has been discussed in detail. Making use of Berry Tabor trace formula, the quantization conditions of the action of the periodic orbits in two dimensional integrable systems have been obtained. Furthermore, considering the periodicity conditions for the periodic orbits on reasonable torus, the correspondence relations between quantum levels and classical periodic orbits in the two dimensional uncoupled oscillators have been established. It is also shown that there exist the long-range correlations among these quantum levels which correspond to the group of the classical periodic orbits with same topology M(M1,M2). To concert state the new points, an example has been given.

References

[1]

. Berry M V ,Tabor M .Proc. R .Soc.,Lond.,1976,A349:101;J. Phys.,1977,A10:3712. Main J. Phys. Rep.,1999,316:233 3. Main J, Wunner G .Phys. Rev. Lett.,1999,82:30384. Haggerty M R et al. Phys. Rev. Lett.,1998,81:15925. Gutzwiller M C J. Math. Phys.,1971,12:343—3586. Ullmo D ,Maurice G ,Steven T .Phys. Rev.,1996,E54:136—152 7. SONG Jian-Jun,LI Xi-Guo.High Energy Phys. and Nucl. Phys.,2001,25(10):958(inChinese)(宋建军,李希国.高能物理与核物理,2001,25(10):958)8. SONG Jian-Jun,Quantization Way in a Two-Dimensional Integrable System and the Long-Range Correlation Among the Quantum Lavels. Master Dissertation, Institute of Modern Physics, CAS ,2001(in Chinese)(宋建军.二维可积系统量子化方案和量子能级中的长程关联.硕士论文,中国科学院近代物理研究所,2001) 9. SONG Jian-Jun, LI Xi-Guo.Acta Physica Sinica,2001,50(10):1661(in Chinese)(宋建军,李希国.物理学报,2001,50(10):1661) 10. Friedrich H ,Wintgen D .Phys. Rep.,1989,183:37 11. Keller J B. Ann. Phys.,1958,4:180—188 12. Wintgen D. Phys. Rev. Lett.,1987,58:1589 13. Bohigas O, Tomsovic S, Ullmo D. Phys. Rep.,1993,223:43

[1]	LIAO Ling , HUANG Yong-Chang . Faddeev-Jackiw Quantization of the Gauge Invariant Self-Dual Fields Relative to String Theory. Chinese Physics C, 2006, 30(3): 191-195.
[2]	LONG Zheng-Wen , LIU Bo , LI Zi-Ping . Canonical Quantization of the Complex Scalar Field Coupled to the Abel Chern-Simons Term. Chinese Physics C, 2003, 27(10): 866-869.
[3]	SONG Jian-Jun , LI Xi-Guo . Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System. Chinese Physics C, 2001, 25(10): 958-963.
[4]	Guo Jianyou , Xu Fuxin , Ruan Tunan . Quantization of Nuclear Hexadecapole Vibration in the Space of Parameter. Chinese Physics C, 1999, 23(9): 873-879.
[5]	Guo Shuohong , Fang Xiyan . Quantization of Lattice Chern-Simons Theory. Chinese Physics C, 1994, 18(8): 706-714.
[6]	Wang Renchuan , Zhu Dongpei . On the Quantization of Interacting Fields in QED. Chinese Physics C, 1994, 18(11): 1012-1019.
[7]	MIAO Yan-Gang . Extension of the Linear Self-Dual Constraint Theory and Its Quantization. Chinese Physics C, 1993, 17(7): 626-630.
[8]	MIAO Yan-Gang . BFV Quantization of the Bosonized Schwinger Model. Chinese Physics C, 1993, 17(5): 407-411.
[9]	HOU Bo-Yu , YANG Huan-Xiong . The Hamiltonian Formalism and Quantizations of (Generalized) BFOFW Model. Chinese Physics C, 1993, 17(6): 524-533.
[10]	MIAO Yan-Gang . Path Integral Light-Cone Quantization of a Gauge Theory of Self-Dual Fields. Chinese Physics C, 1992, 16(7): 596-599.
[11]	SUN Yi , JING Si-Cong , RUAN Tu-Nan . QUANTIZATION OF BOSON STRING WITH WEYL ORDERING. Chinese Physics C, 1989, 13(5): 411-418.
[12]	YU Yue . SYMPLECTIC STRUCTURES AND QUANTIZATION FOR BOSONIC STRINGS IN BRST FORMALISM. Chinese Physics C, 1989, 13(1): 92-96.
[13]	YU Yue , GUO Han-Ying . ON GEOMETRIC QUANTIZATION FOR BOSONIC STRING (Ⅱ). Chinese Physics C, 1989, 13(6): 503-511.
[14]	YU Yue , GUO Han-Ying . ON GEOMETRIC QUANTIZATION FOR THE BOSONIC STRINGS(1). Chinese Physics C, 1989, 13(5): 419-428.
[15]	JING Si-Cong , RUAN Tu-Nan . ON THE QUANTIZATION OF PURE GAUGE FIELDS ON COSET SPACE OF ABELIAN CHIRAL GROUP. Chinese Physics C, 1988, 12(6): 773-781.
[16]	CHEN Ren . STOCHASTIC QUANTIZATION WITH SPIN 3/2 FIELD. Chinese Physics C, 1987, 11(2): 157-163.
[17]	Wu Jing-yuan . QUANTIZATION OF THE PHOTON FIELD AND DIPOLE GHOSTS. Chinese Physics C, 1980, 4(3): 291-301.
[18]	YAN MU-LIN , BAO XI-MING , ZHAO BAO-HENG . CANONICAL QUANTIZATION OF GAUGE FIELDS (Ⅲ)——GRAVITATIONAL FIELD. Chinese Physics C, 1979, 3(5): 582-594.
[19]	GU CHAO-HAO . THE U₁ GAUGE FIELD IN A SU_N GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES. Chinese Physics C, 1978, 2(4): 295-304.
[20]	ZHAO BAO-HENG , YAN MU-LIN . CANONICAL QUANTIZATION OF GAUGE FIELDS (I)——THE YANG-MILLS FIELD. Chinese Physics C, 1978, 2(6): 501-510.

Access

Get Citation

LI Xi-Guo, SONG Jian-Jun, XING Yong-Zhong and ZUO Wei. Quantization of the Periodic Orbits and Long-Range Correlations in Quantum Spectra[J]. Chinese Physics C, 2002, 26(5): 484-490.

LI Xi-Guo, SONG Jian-Jun, XING Yong-Zhong and ZUO Wei. Quantization of the Periodic Orbits and Long-Range Correlations in Quantum Spectra[J]. Chinese Physics C, 2002, 26(5): 484-490. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2001-06-11
Revised: 1900-01-01

Article Metric

Article Views(3140)
PDF Downloads(561)
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

Quantization of the Periodic Orbits and Long-Range Correlations in Quantum Spectra

Corresponding author: LI Xi-Guo,

Research Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Collisions, Lanzhou 730000, China2 Institute of Modern Physics, The Chinese Academy of Sciences, Lanzhou 730000, China

Received Date: 2001-06-11
Accepted Date: 1900-01-01
Available Online: 2002-05-05

Abstract: Using the classical quantization way in a two-dimensional integrable system and quantized energies-periodic orbits correspondence relationship, the long-range correlation among the quantum lavels has been discussed in detail. Making use of Berry Tabor trace formula, the quantization conditions of the action of the periodic orbits in two dimensional integrable systems have been obtained. Furthermore, considering the periodicity conditions for the periodic orbits on reasonable torus, the correspondence relations between quantum levels and classical periodic orbits in the two dimensional uncoupled oscillators have been established. It is also shown that there exist the long-range correlations among these quantum levels which correspond to the group of the classical periodic orbits with same topology M(M1,M2). To concert state the new points, an example has been given.