Spatial-Temporal Evolution of the Wave Packet and Avoided Level Crossing

LIU Fang; LI Jun-Qing

Chinese Physics C> 2002, Vol. 26> Issue(6) : 607-612

Spatial-Temporal Evolution of the Wave Packet and Avoided Level Crossing

LIU Fang ^, ,
LI Jun-Qing

Institute of Modern Physics, Northwest University, Xi'an 710069, China2 Institute of Mordern Physics, The Chinese Academy of Sciences, Lanzhou 730000, China

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Abstract：
In the two cases that the deformed nuclear system is regular and chaotic, the spatial temporal evolution of the coherent states of a two dimensional harmonic oscillator system as an initial state was analyzed with the Fourier transformation, especially by comparing the Fourier transformation of the width of the wave packet in the whole time stage with that the wave packet approaching to the saturation in the chaotic system. It was found that since a large number of avoided level crossings destroy the regular structure of the state space of the system, the components in the wave packet are no longer coherent and the motion of the wave packet becomes chaotic. Afterwards, the contribution coming from the different components tends to uniform, the influence of the avoided level crossings on the motion of the wave packet is not obvious also.

References

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. Gutzwiller M C. Chaos in Classical and Quantum Mechanics, Springer New York, 19902. XU Gong-Ou, YANG Ya-Tian. Chin. Phys. Lett.,1999,16:6—8;XU Gong-Ou et al. Chin. Phys. Lett.,1999,16:82 3. WANG Shun-Jin, CHU S Y. Phys. Rev.,1993,A47(8):3546—3553 4. XU Gong-Ou et al. Phys. Rev.,1992,A45:5401 5. LIU Fang, LI Jun-Qing et al. High Energy Phys. and Nucl. Phys.,2000,24(4):331—336(in Chinese)(刘芳,李君清等.高能物理与核物理,2000,24(4):331—336)6. Heiss W D et al. Phys. Rev. Lett.,1994,72(15):2351—2354 7. LI Jun-Qing. J. Phys.,1998,G24:1021—10288. LIU Fang et al. High Energy Phys. and Nucl. Phys.,1999,23(11):1108—1114;LI Jun-Qing, LIU Fang et al. High Energy Phys.,and Nucl. Phys. 2000,24(4):337(in Chinese)(刘芳等.高能物理与核物理,1999,23(11):1108—1114;李君清,刘芳等.高能物理与核物理,2000,24(4):337) 9. LIU Fang, LI Jun-Qing et al. Comm. Thero. Phys.,2001,35(5):531—538

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LIU Fang and LI Jun-Qing. Spatial-Temporal Evolution of the Wave Packet and Avoided Level Crossing[J]. Chinese Physics C, 2002, 26(6): 607-612.

LIU Fang and LI Jun-Qing. Spatial-Temporal Evolution of the Wave Packet and Avoided Level Crossing[J]. Chinese Physics C, 2002, 26(6): 607-612. shu

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Received: 2001-09-10
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

Spatial-Temporal Evolution of the Wave Packet and Avoided Level Crossing

LIU Fang ^,
LI Jun-Qing

Corresponding author: LIU Fang,

Institute of Modern Physics, Northwest University, Xi'an 710069, China2 Institute of Mordern Physics, The Chinese Academy of Sciences, Lanzhou 730000, China

Received Date: 2001-09-10
Accepted Date: 1900-01-01
Available Online: 2002-06-05

Abstract: In the two cases that the deformed nuclear system is regular and chaotic, the spatial temporal evolution of the coherent states of a two dimensional harmonic oscillator system as an initial state was analyzed with the Fourier transformation, especially by comparing the Fourier transformation of the width of the wave packet in the whole time stage with that the wave packet approaching to the saturation in the chaotic system. It was found that since a large number of avoided level crossings destroy the regular structure of the state space of the system, the components in the wave packet are no longer coherent and the motion of the wave packet becomes chaotic. Afterwards, the contribution coming from the different components tends to uniform, the influence of the avoided level crossings on the motion of the wave packet is not obvious also.