2010 Fiscal Year Final Research Report
Operator-Analytical Study of Singularities Appearing in Quantum Theory
| Project/Area Number |
20540171
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Okayama University |
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Principal Investigator |
HIROKAWA Masao Okayama University, 大学院・自然科学研究科, 教授 (70282788)
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| Co-Investigator(Renkei-kenkyūsha) |
TAMURA Hideo 岡山大学, 大学院・自然科学研究科, 教授 (30022734)
OSHITA Yoshihito 岡山大学, 大学院・自然科学研究科, 准教授 (70421998)
KAWABI Hiroshi 岡山大学, 大学院・自然科学研究科, 准教授 (80432904)
ITO Keiichi 摂南大学, 工学部, 教授 (50268489)
HIROSHIMA Fumio 九州大学, 大学院・数理学研究院, 准教授 (00330358)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 自己共役拡張 / 境界条件 / 位相因子 / 基底状態相転移 / 量子相転移 / エネルギーレベル交差 / 特異性 |
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| Research Abstract |
For the study of quantum physics on the non-Euclidean space, we configured the 1-dim space with a junction, where we supposed many singularities concentrate on the junction. We handled an electron moving in the space with non-relativistic theory. For the electron we investigated the relation of some self-adjoint extensions and corresponding boundary conditions. We found a sufficient condition in order that the boundary condition has a phase factor. As for the property of singularity in quantum field theory, we handled the physical system of a 2-level atom coupled with a 1-mode laser. We study the singularity of the coupling strength which causes the ground state phase transition as one of quantum phase transition. We characterized it with the energy level crossing.
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