2012 Fiscal Year Final Research Report
Spectral asymptotic analysis for Schrodinger operators
| Project/Area Number |
21340037
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Okayama University |
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Principal Investigator |
TAMURA Hideo 岡山大学, 大学院・自然科学研究科, 教授 (30022734)
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| Co-Investigator(Kenkyū-buntansha) |
NAKANO Fumihiko 学習院大学, 理学部, 教授 (10291246)
IWATSUKA Akira 京都工芸繊維大学, 工芸科学研究科, 教授 (40184890)
FUJIIE Seturo 立命館大学, 理工学部, 教授 (00238536)
KAWASHITA Mishio 広島大学, 広島大学, 教授 (80214633)
HIROKAWA Msao 岡山大学, 自然科学研究科, 教授 (70282788)
ADACHI Tadayoshi 神戸大学, 理学研究科, 教授 (30281158)
ICHINOSE Takashi 金沢大学, 名誉教授 (20024044)
KAKEHI Tomoyuki 岡山大学, 自然科学研究科, 教授 (70231248)
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| Co-Investigator(Renkei-kenkyūsha) |
KAWABI Hiroshi 岡山大学, 自然科学研究科, 准教授 (80432904)
MINE Takuya 京都工芸繊維大学, 工芸科学研究科, 准教授 (90378597)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 関数方程式の大域理論 / スペクトル散乱理 / 磁場散乱 / シュレディンガー作用素 / アハラノフ・ボーム効果 / レゾナンス |
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| Research Abstract |
We have studied the Aharonov-Bohm effect (AB effect) in resonances through a simple scattering systemin two dimensions. The system consists of three scatterers, one bounded obstacle and two scalar potentials with compact supports at large separation, where the obstacle is placed between two supports and shields completely the support of a magnetic field. We have obtained that the resonances are generated nearthe real axis by the trajectories trapped between two supports of the scalar potentials and that the location depends heavily on the magnetic flux. This clarifies that the AB effect is deeply involved in resonances for magnetic scattering.
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