| Project/Area Number |
16H03939
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
Obata Nobuaki 東北大学, 情報科学研究科, 教授 (10169360)
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| Co-Investigator(Kenkyū-buntansha) |
瀬川 悦生 東北大学, 情報科学研究科, 准教授 (30634547)
長谷川 雄央 茨城大学, 理工学研究科(理学野), 准教授 (10528425)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥14,690,000 (Direct Cost: ¥11,300,000、Indirect Cost: ¥3,390,000)
Fiscal Year 2018: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Fiscal Year 2017: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Fiscal Year 2016: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
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| Keywords | 量子確率論 / スペクトル解析 / ネットワーク数理 / 量子ウォーク / 確率解析 / 量子ホワイトノイズ / 直交多項式 / グラフスペクトル |
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| Outline of Final Research Achievements |
Non-commutative stochastic analysis, originally as a mathematical framework for statistical problems in quantum physics, has developed providing new aspects and methods for classical problems. We initiated a multi-variate extention of quantum decomposition, which has been a central issue for a long time, through spectral analysis of a pair of strong regular graphs. Some important operators are characterized by differential equations involving quantum white noise derivatives. We studied the graph isomorphism problem in terms of quantum walks and collaborated for application in the field of quantum engineering and quantum physics. By a large scale simulation we examined statistical properties of connected components of the configuration model and found a power law at the critical point with an index which is different from the known results.
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| Academic Significance and Societal Importance of the Research Achievements |
非可換確率解析は量子系の確率解釈に起源をもち、量子物理に動機づけられた諸問題を扱うための厳密な数学的枠組みを与えるのみならず、古典論に属する問題に新しい視点や手法が導入された。古典的な変数の「量子分解」によって現れる非可換代数の構造が、その統計性を司るという原理がいくつかの観点から拡張された。量子現象としての量子ウォーク、ネットワークのスペクトル的特徴づけ、複雑ネットワークの大規模シミュレーションなど、境界領域的な課題を通して周辺領域との研究交流が促進された。これらは基礎科学としての数学に貢献するものと考えられる。
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