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

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

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《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

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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

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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

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Received: 2001-06-11
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

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.