Semi-classical analysis of the Schroedinger equations
| Project/Area Number |
15K04971
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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 analysis
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| Research Institution | Ritsumeikan University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 準古典解析 / 超局所解析 / シュレディンガー作用素 / 量子共鳴 / エネルギー交差 / Schroedinger作用素 / 準古典極限 / 共鳴 / 固有値 / スペクトルシフト関数 / WKB法 / 共鳴極 / WKB解 |
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| Outline of Final Research Achievements |
The main results of the research during this period are the following three. (i) We established a propagation of singularity theorem of the quantum system at a hyperbolic fixed point of the corresponding classical mechanics. We proved that if the semiclassical wave front set is empty on the incoming stable manifold associated to the fixed point, then it is also empty on the outgoing stable manifold. (ii) We prove a theorem that the spectral shift function of the Schroedinger operator with matrix-valued potential has a complete asymptotic expansion if its symbol has a scalar escape function. (iii) We clarified the semiclassical asymptotic distribution of resonances of the Schroedinger operator with matrix-valued potential for a model of one-dimensional 2 by 2 system with an energy level crossing.
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Report
(4 results)
Research Products
(34 results)
