| Project/Area Number |
61540267
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物性一般（含極低温･固体物性に対する理論）
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| Research Institution | Waseda University |
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Principal Investigator |
SAITO N School of Sci. and Eng. Waseda University, 理工学部, 教授 (20063125)
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| Co-Investigator(Kenkyū-buntansha) |
ASAI H School of Sci. and Eng. Waseda University, 理工学部, 教授 (70063584)
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| Project Period (FY) |
1986 – 1987
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| Project Status |
Completed (Fiscal Year 1988)
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| Budget Amount *help |
¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1987: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1986: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | chaotic dynamics / linear response theory / esgsdic heosem / guantum chaos / action integral / membrane potential / convergence in law / 断熱感受率 / ウィグナー分布 / ランダムマトリックス / 生態系 / 不動点の分岐 / ランダム行列 / ストレンジ・アトラクタ / Grassberger-Procaccia法 |
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| Research Abstract |
1. Chaos for the foundation of statistical mechanics.
According to the recent studies of the chaos in hamiltonian systems, the distribution function does not converge in a pointwise manner for t . We thus introduce the concept of convergence in law employed in the theory of probability which claims that the random variables described by the distribution function obey the different probability law from the original one in the limit t . By extending this concept for finite t, we can reformulate the conventional linear response theory. Thus we can remove the several deficiencies and give the foundation of this theory.
We further show that if the limiting distribution function is constant, the system is ergodic. this is an approach to ergodic theory from chaotic dynamics.
2. Quantum Chaos
The origin and nature of quantum chaos is shown to arise from the action integral. This enables us to make a correspondence with the classical one and to relate the behaviors of the energy level and wave functions.
The studies on the energy level spacing, the relation with random matrix and Husiml distribution function are also carried out in connection with quantum chaos.
3. Chaos in biological systems
The chaotic phenomenon observed in biological systems are important for the behaviors of living organisms, and brain research. By analysing the membrane potential of Paramecium the presence of low dimensional chaos is suggested.
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