| Project/Area Number |
09640473
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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 | Nara Women's University |
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Principal Investigator |
TASAKI Shuichi Nara Women's University, Faculty of Science, Associate Professor, 理学部, 助教授 (10260150)
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| Project Period (FY) |
1997 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1999: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1998: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1997: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | distribution function / nonequilibrium state / irreversibility / fractal distribution / singular measure / de Rham equation / quantum chaos / Landauer formula / 間欠性 / レヴィ過程 / C^*代数 / ランダウアー公式 / 緩和モード / SRB測度 / Hopf分岐 / 反応拡散系 / 昇降演算子法 |
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| Research Abstract |
We studied analytically and exactly the behaviors of the distribution functions for dynamical systems including chaotic systems. Following results are obtained : 1)SRB measures for dissipative Baker maps : Invariant distributions and physical measures are constructed with the aid of de Rham's functional equations and their properties are investigated. 2)Microscopic mechanism of dissipation for a MultiBaker map with energy : We introduced a multibaker map with a coordinate corresponding to kinetic energy and studied nonequilibrium stationary states, relaxation modes, scaling-limit behaviors, time evolution towards the past. We found that the dynamical reversibility is consistent with irreversible evolution of distribution functions. 3)Boundary element methods (BEM) for 2d quantum billiards and Fredholm theory : We studied the properties of a functional determinant D(E), which appears in BEM for 2d quantum billiards, and its semiclassical limit with the aid of the Fredholm theory. 4)Quantum nonequilibrium stationary states : We studied the behaviors of a 1d noninteracting electron system placed between two perfect conductors with the aid of CィイD1*ィエD1-algebraic method. Two different stationary states are obtained in the limit of t →±∞. By comparing their properties, the dynamical reversibility is shown to be consistent with irreversible evolution of states. 5)Unstable quantum states : Unstable quantum states can be represented in terms of generalized eigenfunctions of the Hamiltonian such as Gamow vectors. We investigated the properties of two interacting unstable states and necessary mathematical backgrounds.
Also we investigated other related topics such as 6)Optical properties of carbon nanotubes, 7)Spectral properties of evolution operators of distribution functions for Hopf bifurcation and intermittent maps, 8)Transport properties of periodic intermittent maps, and 9)Stationary states for a reaction-diffusion type MultiBaker map.
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