| Project/Area Number |
11166214
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas (A)
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | The Univensity of Tokyo |
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Principal Investigator |
TAKATSUKA Kazuo Graduate School of Arts and Sciences, Professor, 大学院・総合文化研究科, 教授 (70154797)
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| Co-Investigator(Kenkyū-buntansha) |
USHIYAMA Hiroshi Graduate School of Arts and Sciences, Assistant Professor, 大学院・総合文化研究科, 助手 (40302814)
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| Project Period (FY) |
1999 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥38,400,000 (Direct Cost: ¥38,400,000)
Fiscal Year 2001: ¥6,900,000 (Direct Cost: ¥6,900,000)
Fiscal Year 2000: ¥16,000,000 (Direct Cost: ¥16,000,000)
Fiscal Year 1999: ¥15,500,000 (Direct Cost: ¥15,500,000)
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| Keywords | Quantum chaos / semclassical / cluster / mesoscopic science / molecular vibration / プロトン移動 / 表面化学反応 / セルオートマトン / パターン形成 / カオス / 複雑性動力学 / 分子動力学 / 非線形力学 |
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| Research Abstract |
Recently, Takatsuka [1] has proposed a modified semiclassical correlation function that is free of the annoying amplitude factor. We refer this function to the amplitude-free correlation function (AFC), which is written in terms of the Action Decomposed Function [2], AFC is composed of only what we call turn-back orbits. Calculation of the turn-back orbits is by far easier than the periodic orbits. The role of the turn-back orbits in describing a standing wave is physically understandable. As an analogy, one may think of the motion of a string, one of the ends of which is spatially fixed on a wall and the other end is shaken. If the phases of ingoing and outcoming waves reflecting at t = 0 match with each other, they should form a stationary state. Here in this talk, we numerically verify that this theory gives really accurate spectrum in a unified manner both to integrable and nonintegrable systems by showing numerically how the AFC actually reproduces the correct eigenvalues of strongly chaotic systems [3]. This epoch-making method can be readily applied to large systems that could not be quantized otherwise.
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