Operator and Spectral Analyses for Differential Operators with Matrix-Coefficient
| Project/Area Number |
26400117
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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 |
Basic analysis
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
KAWABI Hiroshi 岡山大学, 大学院自然科学研究科, 教授 (80432904)
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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 |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 回路電磁気学 / 一般化された量子ラビ模型 / ディラック粒子 / 接合を持った量子細線 / 深強結合領域 / 一般化された量子Rabi模型 / 仮想光子 / 実光子 / 物理的状態 / 裸の状態 / ラビ模型 / 量子相転移 / Rabi 模型 / Rabi model / Jaynes-Cummings model / energy level crossing |
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| Outline of Final Research Achievements |
In this research program, we considered the following two mathematical models. (1) We studied some quantum effects mainly for the generalized quantum Rabi model among non-commutative harmonic oscillator models. In particular, in the light of circuit QED, we made operator and spectral analyses for that model, and we mathematically clarified its bound state in the deep-strong coupling regime. Meanwhile, (2) for the model of the two quantum wires with a junction between the two, we clarified how the electron's wave function have a phase factor, and how the electron spin has an effect when the electron as a Dirac particle passes through the junction.
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Report
(5 results)
Research Products
(15 results)
