1997 Fiscal Year Final Research Report Summary
The origin of 1/f spectrum fluctuation in the hamiltonian dynamics for lattice systems.
| Project/Area Number |
06640515
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物性一般(含基礎論)
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| Research Institution | Waseda University |
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Principal Investigator |
AIZAWA Yoji Waseda Univ., School of Sci.& Eng., Dept.of Applied Physics, Professor, 理工学部, 教授 (70088855)
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| Co-Investigator(Kenkyū-buntansha) |
HIRAYAMA Takuhisa ATR,researcher, 研究員 (70247229)
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| Project Period (FY) |
1994 – 1996
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| Keywords | hamiltonian chaos / 1 / f spectrum / critical torus / Arnold diffusion / stagnant layr theory / quantum chaos / level statistics |
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| Research Abstract |
The classical and quantum mechanical aspects of hamiltonian chaos have been studied in relation to the 1/f spectral fluctuations in the long time behaviors. The recent results are the followings :
1.The spectral structure of the most stable KAM torus was determined under the nontwist condition.
2.The universality of the 1/f^<mu> spectrum (1<less than or equal>mu<less than or equal>2) was obtained by the computer simulations for the symplectic map in 4 dimensional
3.The relaxation mechanisms of resonace states were theoretically elucidated by the geodesics representation and the subdynamics method.
4.The level statistics for the l/f quantum billiard was obtained by computer simulations, but the mechanism of level repulsions has not yet been elucidated completely.
The preliminary results have been already reported in severeal journals.
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