| Project/Area Number |
19F19315
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| Research Category |
Grant-in-Aid for JSPS Fellows
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| Allocation Type | Single-year Grants |
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| Section | 外国 |
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| Review Section |
Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
首藤 啓 東京都立大学, 理学研究科, 教授 (60206258)
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| Co-Investigator(Kenkyū-buntansha) |
LI JIZHOU 東京都立大学, 理学(系)研究科(研究院), 外国人特別研究員
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| Project Period (FY) |
2019-11-08 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2021: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 2020: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2019: ¥600,000 (Direct Cost: ¥600,000)
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| Keywords | 古典カオス / 一様双曲性 / マルコフ分割 / 高次元シンプレクティック写像 / 馬蹄力学系 / 半古典量子化 / 量子カオス / 安定・不安定多様体 / ホモクニニック軌道 / 半古典論 / 跡公式 / ハミルトン系 / ホモクリニック軌道 / 安定多様体・不安定多様体 / 古典作用 / 軌道間相関 |
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| Outline of Research at the Start |
Purely quantum mechanical phenomena emerging in chaotic systems are studied based on the semiclassical analysis. We especially focus on dynamical localization, which is typically observed in fully chaotic systems, and also examine the mechanicm of quantum tunneling in nonintegrable systems.
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| Outline of Annual Research Achievements |
Our research achievements are twofold. First, by making use of the so called anti-integrable limit, we were able to investigate the topological structure of a four-dimensional Smale horseshoe, which is proposed by our group to be the first generic model of the original Smale horseshoe in two dimensions. Several important properties in two dimensions, such as uniformly hyperbolicity of the dynamics, has already been proven by the members of our group, and a final synthesis of our findings is currently undertaken. Second, my recent discovery has led to a new scheme of constructing the symbolic descriptions of chaotic orbits using a special set of so-called homoclinic orbits as the skeletons of the dynamics. The homoclinic orbits are expected to provide us with critical information on the construction of global Markov partitions for the entire set of the chaotic orbits. Investigations along this line of research is promising to provide us with novel tools that allow us to probe into generic and complicated systems that were otherwise inaccessible using the original Smale horseshoe method. The results will be put into two paper that are currently under preparation: “Symbolic Dynamics of a Four-dimensional Henon Map” and "Global Construction of Markov Partitions with Homoclinic Orbits”.
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| Research Progress Status |
令和3年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
令和3年度が最終年度であるため、記入しない。
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