| Project/Area Number |
26400391
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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 |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Mie University |
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Principal Investigator |
ABE Sumiyoshi 三重大学, 工学研究科, 教授 (70184215)
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| Research Collaborator |
SUZUKI Norikazu
OU Congjie
CHAMBERLIN Ralph V.
LYSOGORSKIY Yury V.
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 非整数運動学 / 変分原理 / 正準形式 / 非整数Fokker-Planck方程式 / 異常拡散 / Hamilton形式 / 劣拡散 / 連続時間ランダムウォーク / エントロピー生成率の下限 / 非ユニタリーダイナミクス |
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| Outline of Final Research Achievements |
The variational principle has been formulated for the fractional Fokker-Planck equation. In the construction of the action integral, the relation has been revealed between the constraint on the normalization condition on a probability distribution and a gauge-theoretic structure associated with the auxiliary field introduced in the action integral.
In addition, the canonical theory has been constructed, and the fractional Fokker-Planck equation has been recast into the form of the Liouville equation. There, a novel problem concerning the presence of two different Hamiltonians has appeared. Regarding this point, the non-equal-time Poisson-Dirac bracket relations have been set up, and, based on them, it has been shown that the two different Hamiltonians actually generate identical time evolution.
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