Analysis of superlattice structure using spectral analysis of non-linear Schroedinger operator
| Project/Area Number |
24540208
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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 |
Global analysis
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| Research Institution | Kanazawa University |
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Principal Investigator |
OGURISU Osamu 金沢大学, 数物科学系, 准教授 (80301191)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | スペクトル解析 / シュレーディンガー作用素 / 離散シュレーディンガー作用素 / 点相互作用 / 量子ウォーク / 関数方程式 / 数理物理 / スペクトル / 負の固有値 / 共鳴 / 離散グラフ / 離散ラプラシアン / δポテンシャル |
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| Outline of Final Research Achievements |
We studied spectral structure of some mathematical models of superlattice semiconductor devices. We studied the relation between the ratio of in-coming and out-going waves and the energy level E for perfect transmission, and found a kind of singularity. We also found that the relation between E and the phase factor, which is mentioned by RT effect, is broken. In another aspect, we introduced and studied the pseudo manifold of potentials for sustainability of resonances or embedded eigenvalues of discrete Schroedinger operator. In addition, we constructed quantum walks on simplicial complex as an application.
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Report
(5 results)
Research Products
(13 results)
