2009 Fiscal Year Final Research Report
Spectrum of Random Schroedinger Operators
| Project/Area Number |
18540125
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kochi University |
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Principal Investigator |
NAKANO Fumihiko Kochi University, 教育研究部自然科学系, 准教授 (10291246)
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| Co-Investigator(Renkei-kenkyūsha) |
MINAMI Nariyuki 慶応大学, 医学部, 教授 (10183964)
UEKI Naomasa 京都大学, 人間環境学科, 准教授 (80211069)
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| Project Period (FY) |
2006 – 2009
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| Keywords | ランダムシュレーディンガー作用素 / アンダーソン局在 / 局在中心 |
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| Research Abstract |
We consider the distribution of eigenvalue and eigenfunction on the localized region of the random Schroednger operator on d-dimensional square lattice. We showed that, (1) they are uniformly distributed, as a whole, (2) they obey Poisson distribution in the natural scaling limit, and (3) they are repulsive under smaller scaling. Moreover, if we have Minami's estimate, the same results also hold for the random Schrodeinger operaors on the continuum.
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