New developments on quantum information theory by an infinite dimensional stochastic analysis and applications to dynamical system theory
| Project/Area Number |
24540149
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Meijo University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MIMACHI Yuko 名城大学, 理工学部, 准教授 (00218629)
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| Co-Investigator(Renkei-kenkyūsha) |
ICHIHARA Kanji 名城大学, 理工学部, 教授 (00112293)
OBATA Nobuaki 東北大学大学院, 情報科学研究科, 教授 (10169360)
HIBINO Yuji 佐賀大学, 工学系研究科, 准教授 (50253589)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 無限次元解析 / 確率解析 / 関数解析 / 量子情報論 / 力学系理論 / 無限次元ラプラシアン / 確率論的数論 / 量子確率論 / 無限次元確率過程 / 数論的確率論 / 分枝過程 / 量子ホワイトノイズ / 無限次元ラプラス作用素 / 無限次元確率解析 / 量子情報解析 / 量子確率過程 / 超函数の積 / 無限次元ブラウン運動の積 / 超汎関数空間 / 符号力学系 / エルゴード理論 |
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| Outline of Final Research Achievements |
①We introduced an infinite dimensional Brownian motions associated with higher real order derivatives of white noise and proved that their generators of this stochastic processes are given by exotic Laplacians. We also proved that higher real order Cesaro Theorem, and that the exotic Laplacian coincides with the Levy Laplacian associated with higher real order derivative of white noise. ② Constructing a space of distributions on which the product is well-defined, we formulated powers of an infinite dimensional Brownian motion without any renormalization as mathematics. This implies a generalization of the Ito formula in stochastic analysis. On the space of distributions the divergent part in the theory of quantum field is also formulated as mathematics. ③ We gave a method of triangulation decomposition of the transition probability matrix of the G-W branching process, and obtained a limiting probability distribution of the process. We also developed a new algorism of the method.
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Report
(4 results)
Research Products
(13 results)
