Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System

SONG Jian-Jun; LI Xi-Guo

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2001, Vol. 25> Issue(10) : 958-963

Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System

SONG Jian-Jun ^, ,
LI Xi-Guo

Research Center of theoretical Nuclear Physics, Teh National Laboratory of Heavy Ion Collision, Lanzhou 730000, China2 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China

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Abstract：
The general quantization condition for periodic orbits in a two-dimensional integrable sys- tem is presented via the Berry-Tabor trace formula. Using the quantization and a periodicity condi- tion of periodic orbits the semiclassical quantization condition and semiclassical quantized energies of a two dimensional uncoupled quartic oscillator system are given in detail. The semiclassical quantized energies-periodic orbits correspondence is also analysed.

References

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Einstein A. Verh. Dtsch. Phys. Ges., 1917, 19: 822 Brillouin L J. Phys. Radium., 1926,7: 3533 Keller J B. Ann. Phys. , 1958,4: 180–188 4 Gutzwiller M C. J. Math. Phys., 1971, 12:343–358 5 Olavo L S F. Physica, 1999, A271: 260–3026 Berry M V,Tabor M. J. Phys., 1977,A10:371–379 7 Ullmo Denis, Grinberg Maurice, Tomsovic Steven. Phys. Rev., 1996, E54: 136–152 8 Hioe F T, MontrollE W, Yamawaki M. Perspectives in Statistical Nuclear Physics , North–Holland: Amsterdam, 1981

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SONG Jian-Jun and LI Xi-Guo. Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System[J]. Chinese Physics C, 2001, 25(10): 958-963.

SONG Jian-Jun and LI Xi-Guo. Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System[J]. Chinese Physics C, 2001, 25(10): 958-963. shu

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Received: 2000-10-17
Revised: 1900-01-01

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Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System

SONG Jian-Jun ^,
LI Xi-Guo

Corresponding author: SONG Jian-Jun,

Research Center of theoretical Nuclear Physics, Teh National Laboratory of Heavy Ion Collision, Lanzhou 730000, China2 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China

Received Date: 2000-10-17
Accepted Date: 1900-01-01
Available Online: 2001-10-05

Abstract: The general quantization condition for periodic orbits in a two-dimensional integrable sys- tem is presented via the Berry-Tabor trace formula. Using the quantization and a periodicity condi- tion of periodic orbits the semiclassical quantization condition and semiclassical quantized energies of a two dimensional uncoupled quartic oscillator system are given in detail. The semiclassical quantized energies-periodic orbits correspondence is also analysed.